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Chapter 12: Q. 45 (page 954)

Find all points where the first-order partial derivatives of the functions in Exercises 43-54are continuous. Then use Theorems 12.28and 12.31to determine the sets in which the functions are differentiable.

f(x,y)=xx2+y2-1

Short Answer

Expert verified

The sets is S1=(x,y)鈭�x2+y2鈮�1and differentiable withS1all points.

Step by step solution

01

Partial derivatives of function

Given function is,

f(x,y)=xx2+y2-1

So the partial derivatives of function are,

ddxf(x,y)=-x2-y2+1x2+y2-12Andddyf(x,y)=-2xyx2+y2-12

02

Explanation

Where x2+y2鈮�1, these partial derivatives are continuous.

They're continuous on the setS1=(x,y)鈭�x2+y2鈮�1,

And the function is differentiable at all points inS1.

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