   Chapter 7.4, Problem 35E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding and Evaluating Partial Derivatives In Exercises 33-40, find the first partial derivatives with respect to x, y, and z, and evaluate each at the given point. w = x 2 + y 2 + z 2 ; ( 2 ,   − 1 , 2 )

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=x2+y2+z2 at point (2,1,2).

Explanation

Given information:

The provided function is w=x2+y2+z2 and the point is (2,1,2).

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided function is,

w=x2+y2+z2

Partially derivative of the function w=x2+y2+z2 with respect to x.

wx=x(x2+y2+z2)=12x2+y2+z2x(x2+y2+z2)=12x2+y2+z2(2x)=xx2+y2+z2

Substitute (x,y,z)=(2,1,2) into the function wx.

wx|(3,4,2)=2(2)2+(1)2+(2)2=24+1+4=23

Partially derivative of the function w=x2+y2+z2 with respect to y.

wy=y(x2+y2+z2)=12x2+y2+z2y(x2+y2+z2)=12x2+y2+z2(2y)=yx2+y2+z2

Substitute (x,y,z)=(2,1,2) into the function wy

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