Answer
$x^x (1+\ln x) $
Work Step by Step
We have: $y=x^x$
We need to take natural logarithm of both sides.
$\ln y=x \ln x$
We differentiate both sides with respect to $x$.
$ \dfrac{1}{y}\dfrac{dy}{dx}=x \times \dfrac{1}{x}+\ln x \\ \dfrac{dy}{dx}=y(1+\ln x) \\ \dfrac{dy}{dx}=x^x (1+\ln x) $
