MATE CCSS II/Tema 6-Cálculo de derivadas Ariketa-1-1 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-10 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mfenced»«mrow»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfenced»«mn»3«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msup><mfenced><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>3</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-11 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mfenced»«mrow»«mn»2«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»10«/mn»«/mrow»«/mfenced»«mn»4«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msup><mfenced><mrow><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow></mfenced><mn>4</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>192</mn><mo>*</mo><msup><mi>x</mi><mn>11</mn></msup><mo>-</mo><mn>1600</mn><mo>*</mo><msup><mi>x</mi><mn>9</mn></msup><mo>+</mo><mn>2880</mn><mo>*</mo><msup><mi>x</mi><mn>8</mn></msup><mo>+</mo><mn>4800</mn><mo>*</mo><msup><mi>x</mi><mn>7</mn></msup><mo>-</mo><mn>16800</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mn>8400</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>30000</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>45500</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9000</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>30000</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>20000</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2112</mn><mo>*</mo><msup><mi>x</mi><mn>10</mn></msup><mo>-</mo><mn>14400</mn><mo>*</mo><msup><mi>x</mi><mn>8</mn></msup><mo>+</mo><mn>23040</mn><mo>*</mo><msup><mi>x</mi><mn>7</mn></msup><mo>+</mo><mn>33600</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>100800</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>42000</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>120000</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>136500</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>18000</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30000</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-12 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mfenced»«mrow»«mi»a«/mi»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-13 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-14 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>19</mn><mrow><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>30</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>114</mn></mrow><mrow><mn>27</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>135</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>225</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>125</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-15 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><msup><mi>x</mi><mn>3</mn></msup><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>8</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-16 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><msup><mi>x</mi><mn>2</mn></msup><mn>5</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-17 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></mrow></msqrt></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mrow><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></mrow></msqrt></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-18 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>5</mn></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></msqrt></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mo>*</mo><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></msqrt></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-19 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msqrt><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mn>3</mn></mfrac></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mn>6</mn><mo>*</mo><msqrt><mrow><mfrac><mi>x</mi><mn>3</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></msqrt></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mfenced><mrow><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></mrow></mfenced><mo>*</mo><msqrt><mrow><mfrac><mi>x</mi><mn>3</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></msqrt></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-2 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-20 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f


Emaitza arrazionalizatu.

Racionaliza la respuesta.

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow><mn>3</mn></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><mroot><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow><mn>3</mn></mroot></mrow><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn></mrow></mfenced><mo>*</mo><mroot><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow><mn>3</mn></mroot></mrow><mrow><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>18</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-21 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfenced»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»7«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»12«/mn»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>12</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>57</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>84</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>114</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-22 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msqrt><mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><mrow><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><msqrt><mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></msqrt></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow><mrow><mfenced><mrow><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><msqrt><mfrac><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfrac></msqrt></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-23 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f

Arrazionalizatu emaitza.

Racionaliza la solución.

]]> 1.0000000 0.3333333 0 0 f'(x)=#df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>7</mn><mi>x</mi></mrow><mn>5</mn></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow></mfenced><mo>*</mo><mroot><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi></mrow><mn>5</mn></mroot></mrow><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>35</mn><mo>*</mo><mi>x</mi></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>42</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>196</mn></mrow></mfenced><mo>*</mo><mroot><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi></mrow><mn>5</mn></mroot></mrow><mrow><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>350</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>1225</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-24 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)=#df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>12</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>84</mn></mrow><mrow><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>14</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>49</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>210</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>28</mn></mrow><mrow><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>21</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>147</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>343</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-25 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)=#df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>x</mi><mo>+</mo><msqrt><mrow><mn>1</mn><mo>-</mo><mi>x</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msqrt><mo>-</mo><mn>1</mn></mrow><mrow><mn>2</mn><mo>*</mo><msqrt><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mfenced><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><msqrt><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-26 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)=#df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>x</mi><mo>*</mo><msup><exponentiale/><mrow><mo>-</mo><mi>x</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><mo>-</mo><mi>x</mi></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><mo>-</mo><mi>x</mi></mrow></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-27 Kalkulatu ondorengo funtzioaren lehen deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)=#df1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><exponentiale/><mrow><mo>-</mo><mi>x</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>f</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>derivar</mi><mo>(</mo><mi>df1</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><mo>-</mo><mi>x</mi></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>*</mo><msup><exponentiale/><mrow><mo>-</mo><mi>x</mi></mrow></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-3 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-4 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>8</mn><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-5 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-6 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-7 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-8 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>3</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>12</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Ariketa-1-9 Kalkulatu ondorengo funtzioaren lehen eta bigarren deribatua, deribazio erregelak erabiliz:

(Calcula, utilizando las reglas de derivación, la primera y segunda derivada de la siguiente función:


f(x)= #f

]]> 1.0000000 0.3333333 0 0 f'(x)= #df1f''(x)= #df2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi><mo>=</mo><mfenced><mi>f</mi></mfenced><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi><mo>=</mo><mi>df1</mi><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>df2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><msup><mi>f</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>&#160;</mo><mo>#</mo><mi mathvariant="normal">d</mi><mi>f</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question>