Derivative of a large product I need help computing 
$$
\frac{d}{dx}\prod_{n=1}^{2014}\left(x+\frac{1}{n}\right)\biggr\rvert_{x=0}
$$
The answer provided is $\frac{2015}{2\cdot 2013!}$, however, I do not know how to arrive at this answer. Does anyone have any suggestions?

HINT:
Write $\prod_{n=1}^{2014}\left(x+\frac1n\right)=e^{\sum_{n=1}^{2014}\log\left(x+\frac1n\right)}$
Can you proceed now?
