Question

If (sin y)^x = (sin x)^y find dy/dx

Answer 1

Step-by-step explanation:

Taking log

xlog(siny) = ylog(sinx)

D . w . r . to . x

= x*(1/siny)cosy*dy/dx + log(siny) = y*(1/sinx)*cosx

+ log(sinx)*dy/dx

= xCoty*dy/dx + log(siny) = yCotx + log(sinx)dy/dx

=> dy/dx{xCoty+log(sinx)} = yCotx - log(siny)

dy/dx = {yCotx - log(siny)/xCoty + log(sinx)}