Explanation Consider the given function, f ( x , y ) = ( 7 e x + 2 y + 4 ) ( e x 2 + y 2 + 2 ) . To find f x ( x , y ) differentiate the f ( x , y ) with respect to x by holding y . f x ( x , y ) = ∂ ∂ x ( 7 e x + 2 y + 4 ) ( e x 2 + y 2 + 2 ) Apply the product rule of partial derivative with respect to x , ∂ ∂ x ( 7 e x + 2 y + 4 ) ( e x 2 + y 2 + 2 ) = ( 7 e x + 2 y + 4 ) ∂ ∂ x ( e x 2 + y 2 + 2 ) + ( e x 2 + y 2 + 2 ) ∂ ∂ x ( 7 e x + 2 y + 4 ) = ( 7 e x + 2 y + 4 ) ( ∂ ∂ x e x 2 + ∂ ∂ x y 2 + ∂ ∂ x 2 ) + ( e x 2 + y 2 + 2 ) ( 7 ∂ ∂ x e x + 2 y + ∂ ∂ x 4 ) = ( 7 e x + 2 y + 4 ) ( e x 2 ∂ ∂ x x 2 + 0 + 0 ) + ( e x 2 + y 2 + 2 ) ( 7 e x + 2 y ∂ ∂ x ( x + 2 y ) ) = ( 7 e x + 2 y + 4 ) ( 2 x e x 2 ) + ( e x 2 + y 2 + 2 ) ( 7 e x + 2 y ) Thus, f x ( x , y ) = ( 7 e x + 2 y + 4 ) ( 2 x e x 2 ) + ( e x 2 + y 2 + 2 ) ( 7 e x + 2 y ) Substitute 2 for x and − 1 for y in the function. f x ( 2 , − 1 ) = ( 7 e 2 + 2 ( − 1 ) + 4 ) ( 2 ( 2 ) e ( 2 ) 2 ) + ( e ( 2 ) 2 + ( − 1 ) 2 + 2 ) ( 7 e 2 + 2 ( − 1 ) ) = ( 7 e 0 + 4 ) ( 2 ( 2 ) e 4 ) + ( e 4 + 3 ) ( 7 e 0 ) = 44 e 4 + 7 e 4 + 21 = 51 e 4 + 21 To find f y ( x , y ) differentiate the f ( x , y ) with respect to y by holding x . f y ( x , y ) = ∂ ∂ y ( 7 e x + 2 y + 4 ) ( e x 2 + y 2 + 2 ) . Apply the product rule of partial derivative with respect to y ,

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ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 9.2, Problem 20E

To determine

To find:

The fx(x,y) and fy(x,y) then find fx(2,−1) and fy(−4,3) for f(x,y)=(7ex+2y+4)(ex2+y2+2).

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Chapter 9.2, Problem 19E

Chapter 9.2, Problem 21E

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Chapter 9 Solutions

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The f x ( x , y ) and f y ( x , y ) then find f x ( 2 , − 1 ) and f y ( − 4 , 3 ) for f ( x , y ) = ( 7 e x + 2 y + 4 ) ( e x 2 + y 2 + 2 ) .

Solution Summary: The author explains that the partial derivative function f_x(x,y) is

To find:

The fx(x,y) and fy(x,y) then find fx(2,−1) and fy(−4,3) for f(x,y)=(7ex+2y+4)(ex2+y2+2).

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Chapter 9 Solutions

The f x ( x , y ) and f y ( x , y ) then find f x ( 2 , − 1 ) and f y ( − 4 , 3 ) for f ( x , y ) = ( 7 e x + 2 y + 4 ) ( e x 2 + y 2 + 2 ) .

Solution Summary: The author explains that the partial derivative function f_x(x,y) is

To find: The fx(x,y) and fy(x,y) then find fx(2,−1) and fy(−4,3) for f(x,y)=(7ex+2y+4)(ex2+y2+2).

Want to see the full answer?

Chapter 9 Solutions

To find:

The fx(x,y) and fy(x,y) then find fx(2,−1) and fy(−4,3) for f(x,y)=(7ex+2y+4)(ex2+y2+2).