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!

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- Jun 19th 2010, 10:28 PMmitchswLeibniz 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! - Jun 19th 2010, 11:17 PMp0oint
Differentiate both sides of the first equation.

- Jun 19th 2010, 11:52 PMmitchsw
...I'm sorry? Could you be any clearer?

- Jun 20th 2010, 04:48 AMHallsofIvy
$\displaystyle \int_0^x e^{x- t}dt= e^x\int_0^x e^{-t}dt$

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