   Chapter 7.4, Problem 28E ### 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 Slopes in the x- and y-Directions In Exercises 25-28, find the slopes of the surface at the given point in (a) the x-direction and (b) the y-direction. See Example 3. x = x 2 + y 2 ( − 2 , 1 , 3 ) (a)

To determine

To calculate: The slope of the surface z=x2y2 in x direction at the point (2,1,3).

Explanation

Given information:

The provided function is z=x2y2 and the point is (2,1,3).

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,

z=x2y2

Partially derivative of the function z=x2y2 with respect to x.

zx=x(x2y2)=x(x2)

(b)

To determine

To calculate: The slope of the surface z=x2y2 in y direction at the point (2,1,3).

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