# Leibniz rule proof

• June 19th 2010, 10:28 PM
mitchsw
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!
• June 19th 2010, 11:17 PM
p0oint
Differentiate both sides of the first equation.
• June 19th 2010, 11:52 PM
mitchsw
...I'm sorry? Could you be any clearer?
• June 20th 2010, 04:48 AM
HallsofIvy
$\int_0^x e^{x- t}dt= e^x\int_0^x e^{-t}dt$

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