Cálculo/Control 3/Fácil C2 - JG_C2_1 CII - Derivadas segundo orden - mixta 1 - F Pregunta: CII - Derivadas segundo orden - mixta 1 - F

Determine la derivada parcial de segundo orden «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»f«/mi»«mrow»«mi»x«/mi»«mi»y«/mi»«/mrow»«/msub»«/math» para la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«/math»#f en el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»y«/mi»«mn»0«/mn»«mo»)«/mo»«/math» .

]]> 1.0000000 0.3333333 0 0 #sol <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>fx</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><mo> </mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><mo> </mo><msup><exponentiale/><mi>x</mi></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fy</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><mo> </mo><mn>2</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>,</mo><mo> </mo><msup><exponentiale/><mrow><mn>2</mn><mo>*</mo><mi>y</mi></mrow></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><mi>fx</mi><mo>*</mo><mi>fy</mi><mo>,</mo><mo> </mo><mn>4</mn><mo>*</mo><mi>fx</mi><mo>*</mo><mi>fy</mi><mo>,</mo><mi>fx</mi><mo>*</mo><mo>(</mo><mi>fx</mi><mo>+</mo><mi>fy</mi><mo>)</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dfx</mi><mo> </mo><mo>=</mo><apply><diff/><bvar><mi>x</mi></bvar><mi>f</mi></apply><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dfxy</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>=</mo><apply><diff/><bvar><mi>y</mi></bvar><mi>dfx</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mi>dfxy</mi><mo>(</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> C3 - JG_2 Derivadas Parciales orden 2 - 2 - F Pregunta: CII - Derivadas Parciales orden 2 - 2 - F

Determine si es verdadero o falso que para la función «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»f«/mi»«/math» ¿se cumple las derivadas mixtas «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»f«/mi»«mrow»«mi»x«/mi»«mi»y«/mi»«/mrow»«/msub»«/math» e «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»f«/mi»«mrow»«mi»y«/mi»«mi»x«/mi»«/mrow»«/msub»«/math» son iguales?

]]> 1.0000000 1.0000000 0 Verdadero Falso <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>a1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo> </mo><mo>=</mo><mo> </mo><mn>1</mn></mrow><mtable><mtr><mtd><mo> </mo><mo> </mo><mi>f</mi><mo> </mo><mo>=</mo><mo> </mo><mi>x</mi><mo>·</mo><msup><exponentiale/><mi>x</mi></msup><mo>+</mo><mi>y</mi><mo>·</mo><mi>x</mi></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><mi>neg</mi><mo> </mo><mo>=</mo><mo> </mo><mn>100</mn></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo> </mo><mi>cierto</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo> </mo><mo>=</mo><mo> </mo><mi>cos</mi><mo>(</mo><mn>2</mn><mo>·</mo><mi>x</mi><mo>)</mo><mo>·</mo><mi>sin</mi><mo>(</mo><mi>y</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pos</mi><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo> </mo><mo>=</mo><mo> </mo><mi>cierto</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo> </mo><mo>=</mo><mo> </mo><msup><mi>x</mi><mn>2</mn></msup><mo>·</mo><msup><exponentiale/><mrow><mn>3</mn><mo>·</mo><mi>y</mi></mrow></msup></mtd></mtr><mtr><mtd><mi>pos</mi><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo> </mo><mo>=</mo><mi>cierto</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> C3_JG_CII_13 Operaciones de Matrices 1 - F Pregunta: CII - Operaciones de Matrices 1 - F

Determine el resultado de las operaciones siguientes según «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»m«/mi»«mi»a«/mi»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«mi»b«/mi»«/math»

1) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»C«/mi»«mo»=«/mo»«mi»A«/mi»«mo»+«/mo»«mi»B«/mi»«/math» , indique «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»C«/mi»«mn»11«/mn»«/msub»«mo»=«/mo»«/math»{#1}

2) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»D«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»A«/mi»«mo»-«/mo»«mi»B«/mi»«/math» , indique «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»D«/mi»«mn»21«/mn»«/msub»«mo»=«/mo»«/math»{#2}

3)«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»E«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«mn»31«/mn»«mo»§#183;«/mo»«mi»B«/mi»«mo»+«/mo»«mfrac»«mi»A«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»32«/mn»«/mrow»«/mfrac»«/math» , indique «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»E«/mi»«mn»12«/mn»«/msub»«mo»=«/mo»«/math»{#3}

Nota: el primer dígito indica la fila y el segundo la columna

]]> 3.0000000 0.3333333 0 <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>a11</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a12</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a21</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a22</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b11</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b12</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b21</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b22</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c31</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c32</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b11</mi></mtd><mtd><mi>b12</mi></mtd></mtr><mtr><mtd><mi>b21</mi></mtd><mtd><mi>b22</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a11</mi><mo> </mo><mo>+</mo><mo> </mo><mi>b11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><mi>a21</mi><mo>-</mo><mi>b21</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>c31</mi><mo>*</mo><mi>b12</mi><mo>+</mo><mfrac><mi>a12</mi><mi>c32</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> C3_JG_CII_14 Cofactores 1 - F Pregunta: CII - Cofactores 1 - F

Encuentre los cofactores de la matriz «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«mi»a«/mi»«/math» según corresponda:

1) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»C«/mi»«mn»13«/mn»«/msub»«mo»=«/mo»«/math» {#1}

2) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»C«/mi»«mn»12«/mn»«/msub»«mo»=«/mo»«/math» {#2}

3) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»C«/mi»«mn»32«/mn»«/msub»«mo»=«/mo»«/math» {#3}

]]> 3.0000000 0.3333333 0 <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>a11</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a12</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a13</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a21</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a22</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a23</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a31</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a32</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a33</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced><mtable><mtr><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd><mtd><mi>a13</mi></mtd></mtr><mtr><mtd><mi>a21</mi></mtd><mtd><mi>a22</mi></mtd><mtd><mi>a23</mi></mtd></mtr><mtr><mtd><mi>a31</mi></mtd><mtd><mi>a32</mi></mtd><mtd><mi>a33</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a21</mi><mo>*</mo><mi>a32</mi><mo>-</mo><mi>a22</mi><mo>*</mo><mi>a31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>a21</mi><mo>*</mo><mi>a33</mi><mo>-</mo><mi>a23</mi><mo>*</mo><mi>a31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>a11</mi><mo>*</mo><mi>a23</mi><mo>-</mo><mi>a13</mi><mo>*</mo><mi>a21</mi></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> C3_JG_CII_15 Propiedades Determinante 2- F Pregunta: CII - Propiedades Determinante 2- F

Calcule el determinante de la siguiente matriz de 4 filas y columnas.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«mi»a«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <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>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced><mtable><mtr><mtd><mi>a1</mi></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>3</mn><mo>*</mo><mi>a2</mi></mtd><mtd><mi>a3</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mi>a4</mi></mtd><mtd><mn>2</mn><mo>*</mo><mi>a5</mi></mtd><mtd><mi>a6</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="|" open="|"><mi>ma</mi></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> C3_JG_CII_21 Derivada Implícita 1 - F Pregunta: CII - Derivada Implícita 1 - F

Suponga que la ecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»f«/mi»«mi»d«/mi»«mi»i«/mi»«mi»s«/mi»«mi»p«/mi»«mi»l«/mi»«mi»a«/mi»«mi»y«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«/math», define implicitamente a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math» .

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <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>f1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mo> </mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>,</mo><mo> </mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo> </mo><mo>+</mo><mo> </mo><mi>y</mi><mo>,</mo><mo> </mo><mi>x</mi><mo>*</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fdisplay</mi><mo> </mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>f1</mi><mo>-</mo><mi>f2</mi><mo>,</mo><mo> </mo><mo>-</mo><mi>f1</mi><mo>-</mo><mi>f2</mi><mo>,</mo><mo> </mo><mi>f1</mi><mo> </mo><mo>+</mo><mo> </mo><mi>f2</mi><mo>,</mo><mo> </mo><mo>-</mo><mi>f1</mi><mo>+</mo><mi>f2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo> </mo><mo>=</mo><mo> </mo><mi>fdisplay</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mfrac><apply><diff/><bvar><mi>x</mi></bvar><mi>F</mi></apply><apply><diff/><bvar><mi>y</mi></bvar><mi>F</mi></apply></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>