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## Homework Statement

I've got a question more with the structure of how this problem is presented:

If

x^(sin y) = y^(cos x)

Find

[tex]

\frac{dx}{dy}(\frac{pi}{4},\frac{pi}{4})

[/tex]

## Homework Equations

We have been taught to solve by implicit differentiation when a problem looks something like this:

if

**x^3 + 2xy^2 +y^3 =1**

But I've seen some examples online of partial derivatives that present an expression with f (x,y)...but this problem looks different that that also.

The only thing in common is that there is an X and a Y variable.

## The Attempt at a Solution

Im unsure of what to look for to solve this...maybe its not even implicit differentiation.

I am going with setting the expression to 0 ie:

(sin y)

x^

------------- = 0

(cos x)

y^

and then solving implicitly...and then popping in the pi/4 into the equation.

Does this sound like a good idea? Or is my instructor trying to "trick" us ...lol

maybe its implicit differentiation WITH exponential/Logarithmic differentiation? Anyway...

Thanks for any clues.

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