Question

find dy/dx for y=x^1-x

Answer 1

Take logarithms on both sides then you have ln y=(1-x)ln x differentiating both sides we have (1/y)dy/dx=(1-x)/x+ln x(-1) hence dy/dx=y{(1-x)/x-ln x) substitute the value of y and you get the answer @Celestine101

Answer 2

-x^-x(x+x(logx)-1)