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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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.

z = x y

( 1 , 2 , 2 )

Chapter 7.4, Problem 25E, Finding Slopes in the x- and y-Directions In Exercises 25-28, find the slopes of the surface at the

(a)

To determine

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

Explanation

Given information:

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

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,

z=xy

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

zx=x(xy)=y"

(b)

To determine

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

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