Chapter 13.3, Problem 72E

Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770

Chapter
Section

Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770
Textbook Problem

Using First Partial Derivatives In Exercises 69-76, find all values of x and y such that f x = ( x , y ) = 0 and f y = ( x , y ) = 0 simultaneously. f ( x , y ) = ln ( x 2 + y 2 + 1 )

To determine

To calculate: All values of x and y such that fx(x,y)=0 and fy(x,y)=0 simultaneously of the function, f(x,y)=ln(x2+y2+1).

Explanation

Given:

The function is f(x,y)=ln(x2+y2+1). The values of derivatives are fx(x,y)=0 and fy(x,y)=0.

Formula Used:

The derivative of a function eax is, ddxlnx=1x.

Calculation:

The function,

f(x,y)=ln(x2+y2+1) …… (1)

Now differentiate equation (1) with respect to x

fx(x,y,z)=xln(x2+y2+1)=1x2+y2+1x(x2+y2+1)=1x2+y2+1(2x)=2x(x2+y2+1) …… (2)

Now differentiate equation (1) with respect to y,

fy(x,y,z)=

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