Explanation Approach: Let z = f ( x , y ) be a function of two independent variables. Let all indicated limits exist. Then the partial derivative of f with respect to x is, f x ( x , y ) = ∂ f ∂ x And the partial derivative with respect to y is, f y ( x , y ) = ∂ f ∂ y Calculation: Consider the function. f ( x , y ) = − 3 x 2 y 3 + x 3 y ... ( 1 ) Differentiate equation ( 1 ) with respect to x and keep y constant. f x ( x , y ) = ∂ ( − 3 x 2 y 3 + x 3 y ) ∂ x = − 6 x y 3 + 3 x 2 y ... ( 2 ) Differentiate equation ( 2 ) with respect to x and keep y constant

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 9.CR, Problem 38CR

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To find:

The value of fxx(x,y) and fxy(x,y) if f(x,y)=−3x2y3+x3y.

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Chapter 9.CR, Problem 37CR

Chapter 9.CR, Problem 39CR

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The value of f x x ( x , y ) and f x y ( x , y ) if f ( x , y ) = − 3 x 2 y 3 + x 3 y .

Solution Summary: The author explains how z=f(x,y) be a function of two independent variables.

Concept explainers

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To find:

The value of fxx(x,y) and fxy(x,y) if f(x,y)=−3x2y3+x3y.

Want to see the full answer?

Chapter 9 Solutions

The value of f x x ( x , y ) and f x y ( x , y ) if f ( x , y ) = − 3 x 2 y 3 + x 3 y .

Solution Summary: The author explains how z=f(x,y) be a function of two independent variables.

Concept explainers

Videos

To find: The value of fxx(x,y) and fxy(x,y) if f(x,y)=−3x2y3+x3y.

Want to see the full answer?

Chapter 9 Solutions

To find:

The value of fxx(x,y) and fxy(x,y) if f(x,y)=−3x2y3+x3y.