   Chapter 14.3, Problem 4PT

Chapter
Section
Textbook Problem

For f ( x , y ) = ln ( 2 x + 3 y ) , f y x = a) − 6 ( 2 x + 3 y ) 2 b) 3 2 x + 3 y c) 6 2 x + 3 y d) 2 x + 3 y

To determine

The appropriate option for the statement “For f(x,y)=ln(2x+3y), fyx=” from the given options.

Explanation

Given function is f(x,y)=ln(2x+3y).

Differentiate the function f(x,y)=ln(2x+3y) with respect to y as follows.

y(f(x,y))=y(ln(2x+3y))=12x+3yy(2x+3y)                         (ddx(lnx)=1x)=12x+3y(3)y(y)                         (ddx(x)=1)   fy(x,y)=32x+3y

Differentiate the function fy(x,y)=32x+3y with respect to x as follows

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