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

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

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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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MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

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Checkout Lines According to...Ch. 14.1 - Prob. 40E Ch. 14.1 - Prob. 41E Ch. 14.1 - Prob. 42E Ch. 14.1 - Prob. 43E Ch. 14.1 - Prob. 44E Ch. 14.1 - Prob. 45E Ch. 14.1 - Prob. 46E Ch. 14.1 - Prob. 47E Ch. 14.1 - Prob. 48E Ch. 14.2 - Prob. 1CP Ch. 14.2 - Prob. 2CP Ch. 14.2 - Prob. 3CP Ch. 14.2 - Prob. 4CP Ch. 14.2 - Prob. 5CP Ch. 14.2 - Prob. 6CP Ch. 14.2 - Prob. 7CP Ch. 14.2 - Prob. 8CP Ch. 14.2 - Prob. 9CP Ch. 14.2 - Prob. 1E Ch. 14.2 - For each of the given functions, find the...Ch. 14.2 - Prob. 3E Ch. 14.2 - Prob. 4E Ch. 14.2 - Prob. 5E Ch. 14.2 - Prob. 6E Ch. 14.2 - Prob. 7E Ch. 14.2 - Prob. 8E Ch. 14.2 - Prob. 9E Ch. 14.2 - Prob. 10E Ch. 14.2 - Prob. 11E Ch. 14.2 - Prob. 12E Ch. 14.2 - Prob. 13E Ch. 14.2 - Prob. 14E Ch. 14.2 - Prob. 15E Ch. 14.2 - Prob. 16E Ch. 14.2 - Prob. 17E Ch. 14.2 - Prob. 18E Ch. 14.2 - Prob. 19E Ch. 14.2 - Prob. 20E Ch. 14.2 - Prob. 21E Ch. 14.2 - Prob. 22E Ch. 14.2 - Prob. 23E Ch. 14.2 - Prob. 24E Ch. 14.2 - Prob. 25E Ch. 14.2 - Prob. 26E Ch. 14.2 - Prob. 27E Ch. 14.2 - Prob. 28E Ch. 14.2 - Prob. 29E Ch. 14.2 - Prob. 30E Ch. 14.2 - Prob. 31E Ch. 14.2 - Prob. 32E Ch. 14.2 - Prob. 33E Ch. 14.2 - Prob. 34E Ch. 14.2 - Prob. 35E Ch. 14.2 - Prob. 36E Ch. 14.2 - Prob. 37E Ch. 14.2 - Find fx,fy,fz, and fyz for the given functions. 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Find positive numbers x and y whose sum is 80...Ch. 14 - Prob. 52RE Ch. 14 - Prob. 53RE Ch. 14 - Prob. 54RE Ch. 14 - Prob. 1CE Ch. 14 - Prob. 2CE

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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