Explanation Approach: To find f x ( x , y , z ) , differentiate f ( x , y , z ) with respect to x by holding y and z , f x ( x , y , z ) = ∂ ∂ x f ( x , y , z ) To find f y ( x , y , z ) , differentiate f ( x , y , z ) with respect to y by holding x and z , f y ( x , y , z ) = ∂ ∂ y f ( x , y , z ) To find f z ( x , y , z ) , differentiate the f ( x , y , z ) with respect to z by holding x and y , f z ( x , y , z ) = ∂ ∂ z f ( x , y , z ) The quotient rule of partial derivative with respect to x , ∂ ∂ x [ f ( x , y , z ) h ( x , y , z ) ] = h ( x , y , z ) ∂ ∂ x f ( x , y , z ) − f ( x , y , z ) ∂ ∂ x h ( x , y , z ) [ h ( x , y , z ) ] 2 The quotient rule of partial derivative with respect to y , ∂ ∂ y [ f ( x , y , z ) h ( x , y , z ) ] = h ( x , y , z ) ∂ ∂ y f ( x , y , z ) − f ( x , y , z ) ∂ ∂ y h ( x , y , z ) [ h ( x , y , z ) ] 2 The quotient rule of partial derivative with respect to z , ∂ ∂ z [ f ( x , y , z ) h ( x , y , z ) ] = h ( x , y , z ) ∂ ∂ y f ( x , y , z ) − f ( x , y , z ) ∂ ∂ y h ( x , y , z ) [ h ( x , y , z ) ] 2 Calculation: Consider the given function, f ( x , y , z ) = 6 x − 5 y 4 z + 5 To find f x ( x , y , z ) , differentiate f ( x , y , z ) with respect to x by holding y and z , f x ( x , y , z ) = ∂ ∂ x ( 6 x − 5 y 4 z + 5 ) Apply the quotient rule of derivative, ∂ ∂ x ( 6 x − 5 y 4 z + 5 ) = ( 4 z + 5 ) ∂ ∂ x ( 6 x − 5 y ) − ( 6 x − 5 y ) ∂ ∂ x ( 4 z + 5 ) [ 4 z + 5 ] 2 = ( 4 z + 5 ) ( 6 ) − ( 6 x − 5 y ) ( 0 ) [ 4 z + 5 ] 2 = 6 ( 4 z + 5 ) Thus, f x ( x , y , z ) = 6 ( 4 z + 5 ) . To find f y ( x , y , z ) , differentiate f ( x , y , z ) with respect to y by holding x and z , f y ( x , y , z ) = ∂ ∂ y ( 6 x − 5 y 4 z + 5 ) Apply the quotient rule of derivative,

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Question

Chapter 9.2, Problem 43E

To determine

To find:

The following derivatives fy(x,y,z), fy(x,y,z), fz(x,y,z) and fyz(x,y,z) of the function f(x,y,z)=6x−5y4z+5.

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Chapter 9.2, Problem 42E

Chapter 9.2, Problem 44E

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Chapter 9 Solutions

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The following derivatives f y ( x , y , z ) , f y ( x , y , z ) , f z ( x , y , z ) and f y z ( x , y , z ) of the function f ( x , y , z ) = 6 x − 5 y 4 z + 5 .

Solution Summary: The author explains how to find the derivatives f_y(x,y,z),

To find:

The following derivatives fy(x,y,z), fy(x,y,z), fz(x,y,z) and fyz(x,y,z) of the function f(x,y,z)=6x−5y4z+5.

Want to see the full answer?

Chapter 9 Solutions

The following derivatives f y ( x , y , z ) , f y ( x , y , z ) , f z ( x , y , z ) and f y z ( x , y , z ) of the function f ( x , y , z ) = 6 x − 5 y 4 z + 5 .

Solution Summary: The author explains how to find the derivatives f_y(x,y,z),

To find: The following derivatives fy(x,y,z), fy(x,y,z), fz(x,y,z) and fyz(x,y,z) of the function f(x,y,z)=6x−5y4z+5.

Want to see the full answer?

Chapter 9 Solutions

To find:

The following derivatives fy(x,y,z), fy(x,y,z), fz(x,y,z) and fyz(x,y,z) of the function f(x,y,z)=6x−5y4z+5.