Answer
$$ f'(x)=x^{3x}(3\ln x+3).$$
Work Step by Step
Recall that $(e^x)'=e^x$
Recall that $(\ln x)'=\dfrac{1}{x}$
We have
$$ f(x)=(e^{\ln x})^{3x}=e^{3x\ln x}.$$
Now taking the derivative, we get
$$ f'(x)= e^{3x\ln x}(3x\ln x)'=e^{3x\ln x}(3\ln x+3x/x)=e^{3x\ln x}(3x\ln x)'=e^{3x\ln x}(3\ln x+3)=x^{3x}(3\ln x+3).$$
