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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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In Exercises 20-23, find the first partial derivatives and evaluate each at the point ( 2 ,   3 ) .

f ( x , y ) = x 2 + 2 y 2 3 x y + 1

To determine

To calculate: The first partial derivatives for the function f(x,y)=x2+2y23xy+1 and their values at point (2,3).

Explanation

Given Information:

The provided function is f(x,y)=x2+2y23xy+1 and the point is (2,3).

Formula used:

The first partial derivatives of the function z=f(x,y) are,

zx=x[f(x,y)]zx=fx(x,y)

And,

zy=y[f(x,y)]zy=fy(x,y)

Calculation:

Consider the function,

f(x,y)=x2+2y23xy+1

The first partial derivatives of the function are,

x[f(x,y)]=x(x2+2y23xy+1)fx=2x+0310+0=2x3

And,

y[f(x,y)]

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