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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

f ( x ,   y )  =  x 4 y 3 y   +   2

To determine

To calculate: The first partial derivatives for the function f(x,y)=x4y3y+2.

Explanation

Given information:

The provided function is f(x,y)=x4y3y+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,

f(x,y)=x4y3y+2

Partially derivative of the function f(x,y)=x4y3y+2 with respect to x.

fx(x,y)=x(x4y3y+2)=y3y+2x(x4)=y3y+2(4x3)=4x3y3y+2

Partially derivative of the function f(x,y)=x4y3y+2 with respect to y

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