Question

differentiate x^y=e^x,with respect to x

Answer 1

$x^y = e^x\\\\y*Ln\ x=x*Ln\ e=x\\\\y=\frac{x}{Ln\ x}\\\\\frac{dy}{dx}=x*\frac{-1}{(Ln\ x)^2}*(1/x)+\frac{1}{Ln\ x}*1\\\\=\frac{-1+Ln\ x}{(Ln\ x)^2}$