   Chapter 7.4, Problem 37E ### 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 = y 3 z 2 e 2 x 2 ;   ( 1 2 ,   − 1 ,   2 )

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=y3z2e2x2 at point (12,1,2).

Explanation

Given information:

The provided function is w=y3z2e2x2 and the point is (12,1,2).

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=y3z2e2x2

Partially derivative of the function w=y3z2e2x2 with respect to x.

wx=x(y3z2e2x2)=y3z2x(e2x2)=y3z2(e2x24x)=4xy3z2e2x2

Substitute (x,y,z)=(12,1,2) into the function wx.

wx|(12,1,2)=4(12)(1)3(2)2e2(12)2=24e12=8e

Partially derivative of the function w=y3z2e2x2 with respect to y.

wy=y(y3z2e2x2)=z2e2x2y(y3)=z2e2x2(3y2)=3y2z2e2x2

Substitute (x,y,z)=(12,1,2) into the function wy

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