How do you differentiate ##y=x^(x-1)##?

##dy/dx= x^(x-1)*((x-1)/x+lnx)##

##y=x^(x-1)##

##lny = (x-1)*lnx##

##1/ydy/dx= (x-1)*1/x+lnx*1##

##dy/dx= y * ((x-1)*1/x+lnx)##

##dy/dx= x^(x-1)*((x-1)/x+lnx)##