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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 Partial Derivatives In Exercises 29-32, find the first partial derivatives with respect to x ,   y , and  z

. See Example 5.

w   =   x y 2 z 4 +   9 x y     z

To determine

To calculate: The first partial derivatives with respect to x,y and z for the function w=xy2z4+9xyz.

Explanation

Given information:

The provided function is w=xy2z4+9xyz.

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=xy2z4+9xyz

Partially derivative of the function w=xy2z4+9xyz with respect to x.

wx=x(xy2z4+9xyz)=y2z4x(x)+9yx(x)x(z)=y2z4+9y

Partially derivative of the function w=xy2z4+9xyz with respect to y

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