# Math Help - Leibniz rule proof

1. ## Leibniz rule proof

I would appreciate any help I could get with this proof:

http://imgur.com/CHr4j.png

I understand the rule, but I'm not sure what to do when the variable is in the limit.
Thanks!

2. Differentiate both sides of the first equation.

3. ...I'm sorry? Could you be any clearer?

4. $\int_0^x e^{x- t}dt= e^x\int_0^x e^{-t}dt$

Differentiate that using the product rule and the "fundamental theorem of calculus" to integrate the second part (the integral).