Behaviour being used: Adaptive mode
Minimum fraction: 0
Question summary: Let [f colon real numbers squared rightwards arrow real numbers squared] be the function, in rectangular coordinates, that satisfies the equation: [open parentheses x plus # a times y square root of open parentheses x squared plus y squared close parentheses to the power of # b end root close parentheses fraction numerator partial differential f over denominator partial differential x end fraction plus open parentheses y minus # a times x square root of open parentheses x squared plus y squared close parentheses to the power of # b end root close parentheses fraction numerator partial differential f over denominator partial differential y end fraction equals 0] If [F] is the expression of [f] in polar coordinates [Error converting from MathML to accessible text.], check the correct statements (there may be more than one) : The equations relating [F] and [f] are [Error converting from MathML to accessible text.]; If [capital phi left parenthesis x comma y right parenthesis equals open parentheses square root of x squared plus y squared end root comma arctan y over x close parentheses], then [f equals F ring operator capital phi to the power of negative 1 end exponent]; The initial equation can be transformed as [open parentheses cos straight theta plus # a times sin straight theta square root of open parentheses r squared close parentheses to the power of # b end root close parentheses fraction numerator partial differential F over denominator partial differential r end fraction plus open parentheses sin straight theta minus # a times cos straight theta square root of open parentheses r squared close parentheses to the power of # b end root close parentheses fraction numerator partial differential F over denominator partial differential theta end fraction equals 0]; The partial derivatives of [F] satisfy [fraction numerator partial differential F over denominator partial differential r end fraction equals # a times r to the power of # c end exponent times fraction numerator partial differential F over denominator partial differential theta end fraction]; The equation in polar coordinates depends from both [r comma theta]
Right answer summary: The partial derivatives of [F] satisfy [fraction numerator partial differential F over denominator partial differential r end fraction equals # a times r to the power of # c end exponent times fraction numerator partial differential F over denominator partial differential theta end fraction]
Question state: todo