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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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In Exercises 10 and 11, find the first partial derivatives and evaluate each at the point (10, −1).

f ( x , y ) = x x + y

To determine

To calculation: The partial derivative of function f(x,y)=xx+y and its value at (10,1).

Explanation

Given information:

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

Formula used:

The partial derivative of function f(x,y) with respect to respect x.

xf(x,y)=fx(x,y)

The partial derivative of function f(x,y) with respect to respect y.

yf(x,y)=fy(x,y)

Calculation:

Consider function,

f(x,y)=xx+y

Calculate the derivative of function with respect to x,

xf(x,y)=x(xx+y)=x(x+y)122+x+y=x2x+y+x+y

The partial derivative of function f(x,y)=xx+y with respect to respect y.

xf(x,y)=x2x+y+x+y

Substitute, 10 for x and 1 for y in above equation,

xf(10,1)=102101+101=53+3=143

Substitute, 10 for <

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