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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 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 )   =   x 2  -  3 x y  +  y 2 ;   ( 1 ,  - 1 )

To determine

To calculate: The first partial derivatives of the function f(x,y)=x23xy+y2 at the point (1,1).

Explanation

Given information:

The provided function is f(x,y)=x23xy+y2 and the point is (1,1).

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)=x23xy+y2

Partially derivative of the function f(x,y)=x23xy+y2 with respect to x.

zx=fx(x,y)=x(x23xy+y2)=x(x2)3yx(x)+x(y2)=2x3y

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

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P-56RECh-7 P-57RECh-7 P-58RECh-7 P-59RECh-7 P-60RECh-7 P-61RECh-7 P-62RECh-7 P-63RECh-7 P-64RECh-7 P-65RECh-7 P-66RECh-7 P-67RECh-7 P-68RECh-7 P-69RECh-7 P-70RECh-7 P-71RECh-7 P-72RECh-7 P-73RECh-7 P-74RECh-7 P-75RECh-7 P-76RECh-7 P-77RECh-7 P-78RECh-7 P-79RECh-7 P-80RECh-7 P-81RECh-7 P-82RECh-7 P-83RECh-7 P-84RECh-7 P-85RECh-7 P-86RECh-7 P-87RECh-7 P-88RECh-7 P-89RECh-7 P-90RECh-7 P-91RECh-7 P-92RECh-7 P-93RECh-7 P-94RECh-7 P-95RECh-7 P-96RECh-7 P-97RECh-7 P-98RECh-7 P-99RECh-7 P-100RECh-7 P-101RECh-7 P-102RECh-7 P-103RECh-7 P-104RECh-7 P-1TYSCh-7 P-2TYSCh-7 P-3TYSCh-7 P-4TYSCh-7 P-5TYSCh-7 P-6TYSCh-7 P-7TYSCh-7 P-8TYSCh-7 P-9TYSCh-7 P-10TYSCh-7 P-11TYSCh-7 P-12TYSCh-7 P-13TYSCh-7 P-14TYSCh-7 P-15TYSCh-7 P-16TYSCh-7 P-17TYSCh-7 P-18TYSCh-7 P-19TYSCh-7 P-20TYSCh-7 P-21TYSCh-7 P-22TYS

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