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 ) = ( y − 2 ) 2 e x + 2 y ... ( 1 ) Differentiate equation ( 1 ) with respect to x and keep y constant. f x ( x , y ) = ∂ ( ( y − 2 ) 2 e x + 2 y ) ∂ x = ( y − 2 ) 2 e x + 2 y Differentiate equation ( 1 ) with respect to y and keep x constant.

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 9.CR, Problem 32CR

To determine

To find:

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

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Chapter 9.CR, Problem 31CR

Chapter 9.CR, Problem 33CR

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Chapter 9 Solutions

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

Ch. 9.1 - YOUR TURN For the function in Example 1, find...Ch. 9.1 - Prob. 2YT Ch. 9.1 - Prob. 3YT Ch. 9.1 - EXERCISES Let f(x,y)=2x3y+5.Find the following. a....Ch. 9.1 - Prob. 2E Ch. 9.1 - EXERCISES Let h(x,y)=x2+2y2. Find the following....Ch. 9.1 - EXERCISES Let f(x,y)=9x+5ylogx. Find the...Ch. 9.1 - EXERCISES Let f(x,y)=ex+ln(x+y). Find the...Ch. 9.1 - EXERCISES Let f(x,y)=xex+y. Find the following. a....Ch. 9.1 - EXERCISES Let f(x,y)=xsin(x2y). Find the...

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

Solution Summary: The author explains how to find the value of f_x(x,y), if it is a function of two independent variables.

Videos

To find:

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

Want to see the full answer?

Chapter 9 Solutions

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

Solution Summary: The author explains how to find the value of f_x(x,y), if it is a function of two independent variables.

Videos

To find: The value of fx(x,y) and fy(x,y) if f(x,y)=(y−2)2ex+2y.

Want to see the full answer?

Chapter 9 Solutions

To find:

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