Question

find dy/dx if (sinx)^cosy = (siny)^cosx

Answer 1

take log of both sides and then differentiate.

Answer 2

\[\cos y( \ln \sin x)=\cos x~\left( \ln \sin y \right)\]
diff. w.r.t. x
\[\cos y \frac{ \cos x }{ \sin x }+\ln \sin x~\left( -\sin y \right)\frac{ dy }{ dx }=\cos x \frac{ \cos y }{ \sin y }\frac{ dy }{ dx }-\sin x \left( \ln \sin y \right)\]
find\[\frac{ dy }{ dx }\]