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 ,

2nd Edition

ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

See similar textbooks

Videos

Question

Chapter 9.2, Problem 46E

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)=ln|8xy+5yz−x3|

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.2, Problem 45E

Chapter 9.2, Problem 47E

Students have asked these similar questions

Find: lim x →-6 f (x) limx-4 f (x) lim x-1 f (x) lim x →4 f (x) (-6,3) • (-1,5) -8 -7 (-6,-2) 4+ (4,5) (4,2) • (-1,1) -6

3 2 Find: ƒ(1) lim f(x) 14-x 2 ƒ(2) lim f(x) x-2- lim f(x) x+2+ lim f(x) x→4 3 y=f(x)

what can the answer be pls help

Chapter 9 Solutions

EBK CALCULUS FOR THE LIFE SCIENCES

Ch. 9.1 - YOUR TURN For the function in Example 1, find...Ch. 9.1 - Prob. 2YT Ch. 9.1 - Prob. 3YT Ch. 9.1 - EXERCISES Let f(x,y)=2x3y+5.Find the following. a....Ch. 9.1 - Prob. 2E Ch. 9.1 - EXERCISES Let h(x,y)=x2+2y2. Find the following....Ch. 9.1 - EXERCISES Let f(x,y)=9x+5ylogx. Find the...Ch. 9.1 - EXERCISES Let f(x,y)=ex+ln(x+y). Find the...Ch. 9.1 - EXERCISES Let f(x,y)=xex+y. Find the following. a....Ch. 9.1 - EXERCISES Let f(x,y)=xsin(x2y). Find the...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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),

Videos

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),

Videos

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|