Explanation Given information: f x , y , z = x y + z Calculation: Consider the function f x , y , z = x y + z . Differentiate the function with respect to x , y , and z as follows. f x , y , z = x y + z f x = ∂ ∂ x x y + z = 1 y + z f y = ∂ ∂ y x y + z = − x y + z 2 f z = ∂ ∂ z x y + z = − x y + z 2 Now, differentiate f x with respect to x , y , and z as follows. f x x = ∂ ∂ x 1 y + z = 0 f x y = ∂ ∂ y 1 y + z = − 1 y + z 2 f x z = ∂ ∂ z 1 y + z = − 1 y + z 2 Now, differentiate f y with respect to x , y , and z as follows. f y x = ∂ ∂ x − x y + z 2 = − 1 y + z 2 f y y = ∂ ∂ y − x y + z 2 = 2 x y + z 3 f y z = ∂ ∂ z − x y + z 2 = 2 x y + z 3 Now, differentiate f z with respect to x , y , and z as follows

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ISBN: 9780135164884

Author: BITTINGER

Publisher: PEARSON

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Chapter 6.2, Problem 66E

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To find: The value of fxx , fyy , fzz , fxy , fyx , fxz , fzx , fyz , fzy .

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Chapter 6.2, Problem 65E

Chapter 6.2, Problem 67E

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The value of f x x , f y y , f z z , f x y , f y x , f x z , f z x , f y z , f z y .

Solution Summary: The author analyzes the function f(x,y,z)=xy+z.

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To find: The value of fxx , fyy , fzz , fxy , fyx , fxz , fzx , fyz , fzy .

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Chapter 6 Solutions