Compute f'(e) where f(x)=3^(xlnx)

Answer 1

f'(x) = ln3(x(1/x) + lnx)(3^(xlnx))
= ln3(1 + lnx)(3^(xlnx))

so f'(e) = ln3(1+lne)(3^(elne))
= ln3(2)(3^(e))