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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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Find the first partial derivatives of

f ( x , y )   = x 2 y 3 and evaluate each at the point ( 1 ,   2 ) .

To determine

To calculate: The first partial derivatives of the function f(x,y)=x2y3 at the point (1,2).

Explanation

Given information:

The provided function is f(x,y)=x2y3 and the point is (1,2).

Formula used:

The first partial derivatives of z=f(x,y) are represented as,

zx=fx(x,y)=zx=x[fx(x,y)]zy=fy(x,y)=zy=y[fy(x,y)]

The value of first partial derivatives at point (a,b) are represented as,

zx|(a,b)=fx(a,b)zy|(a,b)=fy(a,b)

Calculation:

Consider the provided function is,

f(x,y)=x2y3

Partially derivative of the function f(x,y)=x2y3 with respect to x.

zx=fx(x,y)=x(x2y3)=y3x(x2)=2xy3

Substitute (x,y)=(1,2) in derivative fx(x,y)

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