Explanation Given: The function is f ( x , y , z ) = x 2 y 3 z 5 − 4 x 2 y 5 + 3 x z 6 − 2 y 8 z 7 . Definition used: Partial derivatives: The partial derivative of f with respect to x is the derivative of f obtained by treating x as a variable and y as a constant. The partial derivative of f with respect to y is the derivative of f obtained by treating y as a variable and x as a constant. Calculation: Obtain the partial derivative f x ( x , y ) . f x ( x , y , z ) = ∂ ∂ x ( x 2 y 3 z 5 − 4 x 2 y 5 + 3 x z 6 − 2 y 8 z 7 ) = ∂ ∂ x ( x 2 y 3 z 5 ) − ∂ ∂ x ( 4 x 2 y 5 ) + ∂ ∂ x ( 3 x z 6 ) − ∂ ∂ x ( 2 y 8 z 7 ) = ( y 3 z 5 ) ∂ ∂ x ( x 2 ) − ( 4 y 5 ) ∂ ∂ x ( x 2 ) + ( 3 z 6 ) ∂ ∂ x ( x ) − ∂ ∂ x ( 2 y 8 z 7 ) = ( y 3 z 5 ) ( 2 x 2 − 1 ) − ( 4 y 5 ) ( 2 x 2 − 1 ) + ( 3 z 6 ) ( 1 x 1 − 1 ) − 0 Simplify the terms and obtain the partial derivatives. f x ( x , y , z ) = ( y 3 z 5 ) ( 2 x ) − ( 4 y 5 ) ( 2 x ) + ( 3 z 6 ) = 2 x y 3 z 5 − 8 x y 5 + 3 z 6 Thus, the partial derivative with respect to x is f x ( x , y , z ) = 2 x y 3 z 5 − 8 x y 5 + 3 z 6 . The Partial derivative of function f ( x , y , z ) with respect to y is, f y ( x , y , z ) = ∂ ∂ y ( x 2 y 3 z 5 − 4 x 2 y 5 + 3 x z 6 − 2 y 8 z 7 ) = ∂ ∂ y ( x 2 y 3 z 5 ) − ∂ ∂ y ( 4 x 2 y 5 ) + ∂ ∂ y ( 3 x z 6 ) − ∂ ∂ y ( 2 y 8 z 7 ) = ( x 2 z 5 ) ∂ ∂ y

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

10th Edition

ISBN: 9780133935592

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 17.4, Problem 2WE

To determine

To find: The partial derivatives, fx(x,y),fy(x,y) and fz(x,y) .

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Chapter 17.4, Problem 1WE

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Chapter 17 Solutions

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

Ch. 17.1 - For the function in Example 1, find f(2, 3)....Ch. 17.1 - Prob. 2YT Ch. 17.1 - Prob. 3YT Ch. 17.1 - Prob. 4YT Ch. 17.1 - Prob. 1WE Ch. 17.1 - Prob. 2WE Ch. 17.1 - Prob. 3WE Ch. 17.1 - Prob. 4WE Ch. 17.1 - Prob. 5WE Ch. 17.1 - Prob. 6WE

Ch. 17.1 - Let f(x, y) = 2x 3y + 5. 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The partial derivatives, f x ( x , y ) , f y ( x , y ) and f z ( x , y ) .

Solution Summary: The author explains the partial derivatives of f with respect to x and y.

To find: The partial derivatives, fx(x,y),fy(x,y) and fz(x,y) .

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Chapter 17 Solutions