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 ) Calculation: Consider the given function, f ( x , y , z ) = ln | 8 x y + 5 y z − x 3 | 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 ( ln | 8 x y + 5 y z − x 3 | ) = 1 ( 8 x y + 5 y z − x 3 ) ∂ ∂ x ( 8 x y + 5 y z − x 3 ) = ( 8 y − 3 x 2 ) ( 8 x y + 5 y z − x 3 ) Thus, f x ( x , y , z ) = ( 8 y − 3 x 2 ) ( 8 x y + 5 y z − x 3 ) . 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 ( ln | 8 x y + 5 y z − x 3 | ) = 1 ( 8 x y + 5 y z − x 3 ) ∂ ∂ y ( 8 x y + 5 y z − x 3 ) = 8 x + 5 z ( 8 x y + 5 y z − x 3 ) Thus, f y ( x , y , z ) = 8 x + 5 z ( 8 x y + 5 y z − x 3 ) . To find f z ( x , y , z ) , differentiate f ( x , y , z ) with respect to z by holding x and y ,

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ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 9.2, Problem 46E

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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)=ln|8xy+5yz−x3|

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Chapter 9.2, Problem 45E

Chapter 9.2, Problem 47E

Chapter 9 Solutions

EBK CALCULUS FOR THE LIFE SCIENCES

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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 ) = ln | 8 x y + 5 y z − x 3 |

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

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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)=ln|8xy+5yz−x3|

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 ) = ln | 8 x y + 5 y z − x 3 |

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

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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)=ln|8xy+5yz−x3|

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)=ln|8xy+5yz−x3|