   Chapter 7.4, Problem 33E ### 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 = 2 x z 2 + 3 x y z − 6 y 2 z ; (1, -1, 2)

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=2xz2+3xyz6y2z at point (1,1,2).

Explanation

Given information:

The provided function is w=2xz2+3xyz6y2z and the point is (1,1,2).

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=2xz2+3xyz6y2z

Partially derivative of the function w=2xz2+3xyz6y2z with respect to x.

wx=x(2xz2+3xyz6y2z)=2z2x(x)+3yzx(x)6y2zx(1)=2z2+3yz

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

wx|(1,1,2)=2(2)2+3(1)(2)=86=2

Partially derivative of the function w=2xz2+3xyz6y2z with respect to y.

wy=y(2xz2+3xyz6y2z)=2xz2y(1)+3xzy(y)6zy(y2)=3xz12yz

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

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