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Chapter 12: Q. 49 (page 954)

Find all points where the first-order partial derivatives of the functions in Exercises43-54are continuous. Then use Theorems12.28and12.31to determine the sets in which the functions are differentiable.

f(x,y)=tan(xy)

Short Answer

Expert verified

The set isS1={(x,y)鈭�x,y鈭�鈩�}for a function.

Step by step solution

01

Partial derivatives of function

Given function is,

f(x,y)=tan(xy)

So the partial derivatives of function are,

ddxf(x,y)=ysec2(xy)Andddyf(x,y)=xsec2(xy)

02

Explanation

At all places, these partial derivatives are continuous.

They're continuous on the set S1={(x,y)鈭�x,y鈭�鈩�}, and the function is differentiable at all points inS1.

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