Thread: indefinite integral

Find the indefinite integral of e^(f(x)+ln(f'(x))) dx

I do have the steps from my teacher, but I'm confused about how to get to the first step which is simplifying to e^ f(x) f'(x)
Would anyone mind explaining how to get to this first step as I do understand the rest except this?

Thanks in advance

$\displaystyle e^{(f(x) + ln(f'(x))} = e^{f(x)}e^{ln(f'(x)} = e^{f(x)}f'(x)$

because e^ln(a) = a.