## Calculus (3rd Edition)

$$f'(x)=x^{3x}(3\ln x+3).$$
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 $$f'(x)= e^{3x\ln x}(3x\ln x)'=e^{3x\ln x}(3\ln x+3x/x)=e^{3x\ln x}(3x\ln x)'=e^{3x\ln x}(3\ln x+3)=x^{3x}(3\ln x+3).$$