   Chapter 7.4, Problem 34E ### 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 = 3 x 2 y − 5 x y z + 10 y z 2 ;   ( 3 ,   4 ,   − 2 )

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=3x2y5xyz+10yz2 at point (3,4,2).

Explanation

Given information:

The provided function is w=3x2y5xyz+10yz2 and the point is (3,4,2).

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=3x2y5xyz+10yz2

Partially derivative of the function w=3x2y5xyz+10yz2 with respect to x.

wx=x(3x2y5xyz+10yz2)=3yx(x2)5yzx(x)+10yz2x(1)=6yx5yz

Substitute (x,y,z)=(3,4,2) into the function wx.

wx|(3,4,2)=6(4)(3)5(4)(2)=72+40=112

Partially derivative of the function w=3x2y5xyz+10yz2 with respect to y.

wy=y(3x2y5xyz+10yz2)=3x2y(y)5xzy(y)+10z2y(y)=3x25xz+10z2

Substitute (x,y,z)=(3,4,2) into the function wy

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