Answer
$$ f'(x)=(1+\frac{1}{x})e^{x+\ln x}.$$
Work Step by Step
Recall that $(e^x)'=e^x$
Recall that $(\ln x)'=\dfrac{1}{x}$
Since $ f(x)=e^{x+\ln x}$, then the derivative, using the chain rule, is given by
$$ f'(x)=e^{x+\ln x} (x+\ln x)'=(1+\frac{1}{x})e^{x+\ln x}.$$
