Differentiate: y=x^x

First take log’s each side as it would turn our complicated function into something differentiable by chain rule.
ln y = x*ln x
Then differentiate y with respect to x:
d(ln y)/dx = ln x + 1
1/y * dy/dx = ln x +1
dy/dx = y(ln x +1)
As we know what y is the final result is dy/dx= x^x(ln x +1)