$\displaystyle x^x$

Online Derivative Calculator ? Shows All Steps!
My derivative calculator says to apply the generalized product rule so that:

$\displaystyle x^x*\frac{d}{dx}(ln(x)*x)$

At first I thought it looked kind of like the chain rule however x^x is not the derivative of x^x. The answer output by the derivative calculator matches my solutions manual but I don't understand the steps I think.

Thanks for any responses...

P.S. I the calculator just means the product rule then I am still confused about ln(x) and how ln(x) became a part of the equation.