Question

hints finding the derivative of this function

Answer 1

From Mathematica:
\[\left(a^x\right)^x \left(\log \left(a^x\right)+x \log (a)\right)+a \left(x^x\right)^a (\log (x)+1)+\left(x^a\right)^x \left(\log \left(x^a\right)+a\right) \]