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Math Help - Leibniz rule proof

  1. #1
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    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!
    Attached Thumbnails Attached Thumbnails Leibniz rule proof-chr4j.png  
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  2. #2
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    Differentiate both sides of the first equation.
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  3. #3
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    ...I'm sorry? Could you be any clearer?
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  4. #4
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    \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).
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