# How to differentiate x^(cosx) = y^(sinx) with respect to x

by styxrihocc
Tags: differentiate, respect, xcosx, ysinx
 P: 10 1. The problem statement, all variables and given/known data Differentiate x^(cosx) = y ^(sinx) with respect to x 2. Relevant equations 3. The attempt at a solution I tried using natural logs but im not sure if its correct, if it's wrong please point me to the right direction, thanks x^(cosx) = y^(sinx) ln x^(cosx) = ln y ^(sinx) ln x (cosx) = ln y (sinx) cosx/x - sinx lnx = cosx lny +sinx/y (dy/dx) cosx/x - sinx lnx - cosx lny = sinx/y (dy/dx) (cosx/x - sinx lnx - cosx lny) / (sinx/y) = dy/dx
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P: 6,747
 Quote by styxrihocc 1. The problem statement, all variables and given/known data Differentiate x^(cosx) = y ^(sinx) with respect to x 2. Relevant equations 3. The attempt at a solution I tried using natural logs but im not sure if its correct, if it's wrong please point me to the right direction, thanks x^(cosx) = y^(sinx) ln x^(cosx) = ln y ^(sinx) ln x (cosx) = ln y (sinx) cosx/x - sinx lnx = cosx lny +sinx/y (dy/dx) cosx/x - sinx lnx - cosx lny = sinx/y (dy/dx) (cosx/x - sinx lnx - cosx lny) / (sinx/y) = dy/dx
Your work is correct. You could be slightly less ambiguous with parentheses though.
 P: 10 Thanks.

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