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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 1-14, find the first partial derivatives. See

z = 2 x 3 + 5 y 3

To determine

To calculate: The first partial derivatives for the function z=2x3+5y3.

Explanation

Given information:

The provided function is z=2x3+5y3.

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=2x3+5y3

Partially derivative of the function z=2x3+5y3 with respect to x.

zx=x(2x3+5y3)=13(2x3+5y)23(6x2)=136x2(2x3+5y)23=2x2(2x3+5y)23

Partially derivative of the function z=2x3+5y3 with respect to x

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