   Chapter 7.4, Problem 36E ### 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

# 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 = 3 x 2 + y 2 − 2 z 2 ; ( 1 ,   − 2 ,   1 )

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=3x2+y22z2 at point (1,2,1).

Explanation

Given information:

The provided function is w=3x2+y22z2 and the point is (1,2,1).

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=3x2+y22z2

Partially derivative of the function w=3x2+y22z2 with respect to x.

wx=x(3x2+y22z2)=123x2+y22z2x(3x2+y22z2)=123x2+y22z2(6x)=3x3x2+y22z2

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

wx|(1,2,1)=313(1)2+(2)22(1)2=33+42=3555=355

Partially derivative of the function w=3x2+y22z2 with respect to y.

wy=y(3x2+y22z2)=123x2+y22z2y(3x2+y22z2)=123x2+y22z2(2y)=y3x2+y22z2

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

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