Explanation Given: The algebraic expression f ( x , y , z ) = 9 y e 3 x z 4 . Formula Used: Chain rule: If f = f ( u ) and u = u ( x ) , then the derivative of function f with respect to x is, d f d x = d f d u ⋅ d u d x Calculation: Consider the expression, f ( x , y , z ) = 9 y e 3 x z 4 To determine the partial derivative with respect to x , consider x as variable and y , z as constants. Let f = e u and u = 3 x z 4 . Now to find the derivative, apply the chain rule, d f d x = d f d u ⋅ d u d x . Therefore, ∂ f ∂ x = ∂ ∂ x ( 9 y e 3 x z 4 ) = 9 y ⋅ e 3 x z 4 ⋅ 3 z 4 = 27 y z 4 e 3 x z 4 Thus, f x = 27 y z 4 e 3 x z 4 . Next, to determine the partial derivative with respect to y , consider y as variable and x , z as constants. Apply the chain rule, d f d x = d f d u ⋅ d u d x . Therefore, ∂ f ∂ y = ∂ ∂ y ( 9 y e 3 x z 4 ) = 9 e 3 x z 4 Thus, f y = 9 e 3 x z 4

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ISBN: 9780134776323

Author: MULLINS

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 14.2, Problem 37E

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To calculate: Partial derivatives fx, fy, fz, fyz for the function f(x,y,z)=9ye3xz4.

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Chapter 14.2, Problem 36E

Chapter 14.2, Problem 38E

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Chapter 14 Solutions

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Partial derivatives f x , f y , f z , f y z for the function f ( x , y , z ) = 9 y e 3 x z 4 .

Solution Summary: The author calculates the partial derivative of the algebraic expression f(x,y,z)=9ye3xz4.

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To calculate: Partial derivatives fx, fy, fz, fyz for the function f(x,y,z)=9ye3xz4.

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Chapter 14 Solutions