e^y=y^x
=> y loge=xlogy
=> y =xlogy
=> dy/dx=x/y(dy/dx)+logy
=> dy/dx=(1/logy)(dy/dx)+logy
=> dy/dx-(1/logy)(dy/dx)=logy
=> (dy/dx)(1-1/logy)=logy
=> (dy/dx)(logy-1)/logy=logy
=> (dy/dx)=(logy)^2/(logy-1)
proved
