Explanation Given: The function, f ( x , y , z ) = x 3 y + y 3 z + z 3 x Concept Used: While finding the partial derivative with respect to any one variable, assume other variables as constants. Calculation: In order to find the function g ( x , y , z ) , first find the partial derivative and then substitute in the given equation. On differentiating f ( x , y , z ) with respect to x , by treatingy and zas constant, it gives ∂ f ∂ x = ∂ ∂ x ( x 3 y + y 3 z + z 3 x ) = ∂ ∂ x ( x 3 y ) + ∂ ∂ x ( y 3 z ) + ∂ ∂ x ( z 3 x ) = 3 x 2 ⋅ y + 0 + z 3 ⋅ 1 = 3 x 2 y + z 3 Similarly, on differentiating f ( x , y , z ) with respect to y , by treating x and z as constant, it gives ∂ f ∂ y = ∂ ∂ y ( x 3 y + y 3 z + z 3 x ) = ∂ ∂ y ( x 3 y ) + ∂ ∂ y ( y 3 z ) + ∂ ∂ y ( z 3 x ) = x 3 ⋅ 1 + 3 y 2 ⋅ z + 0 = x 3 + 3 y 2 z And, on differentiating f ( x , y , z ) with respect to z , by treating x and y as constant, it gives ∂ f ∂ z =

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 11, Problem 57SP

To determine

The function g(x, y, z) , such that

∂f∂x+∂f∂y+∂f∂z=x3+y3+z3+3g(x,y,z)

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Chapter 11, Problem 56SP

Chapter 11, Problem 58SP

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Chapter 11 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

Ch. 11.1 - Prob. 1PS Ch. 11.1 - Prob. 2PS Ch. 11.1 - Prob. 3PS Ch. 11.1 - Prob. 4PS Ch. 11.1 - Prob. 5PS Ch. 11.1 - Prob. 6PS Ch. 11.1 - Prob. 7PS Ch. 11.1 - Prob. 8PS Ch. 11.1 - Prob. 9PS Ch. 11.1 - Prob. 10PS

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The function g ( x , y , z ) , such that ∂ f ∂ x + ∂ f ∂ y + ∂ f ∂ z = x 3 + y 3 + z 3 + 3 g ( x , y , z )

Solution Summary: The author explains how to find the function g(x,y), assuming other variables as constants.

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The function g(x, y, z) , such that

∂f∂x+∂f∂y+∂f∂z=x3+y3+z3+3g(x,y,z)

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Chapter 11 Solutions

The function g ( x , y , z ) , such that ∂ f ∂ x + ∂ f ∂ y + ∂ f ∂ z = x 3 + y 3 + z 3 + 3 g ( x , y , z )

Solution Summary: The author explains how to find the function g(x,y), assuming other variables as constants.

Videos

The function g(x, y, z) , such that ∂f∂x+∂f∂y+∂f∂z=x3+y3+z3+3g(x,y,z)

Want to see the full answer?

Chapter 11 Solutions

The function g(x, y, z) , such that

∂f∂x+∂f∂y+∂f∂z=x3+y3+z3+3g(x,y,z)