   Chapter 7.4, Problem 17E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding and Evaluating Partial Derivatives In Exercises 17-24, find the first partial derivatives and evaluate each at the given point. See Example 2. f ( x ,   y )   =   3 x 2 +   x y   –   y 2 ;   ( 2 ,   1 )

To determine

To calculate: The first partial derivatives of the function f(x,y)=3x2+xyy2 at the point (2,1).

Explanation

Given information:

The provided function is f(x,y)=3x2+xyy2 and the point is (2,1).

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)=3x2+xyy2

Partially derivative of the function f(x,y)=3x2+xyy2 with respect to x.

zx=fx(x,y)=x(3x2+xyy2)=3x(x2)+yx(x)x(y2)=6x+y

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

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