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Math Help - Leibniz Rule - quick question

  1. #1
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    Leibniz Rule - quick question

    I'm working through an example following Leibniz rule...but havning trouble following it:

    We differentiate:



    using Leibniz's Rule:



    So just looking at the first integral,

    I don't understand the b'(x)f(x,b(x)) part of the rule. Here b(x) = x so b'(x) = 1. But for f(x,b(x)) this would become f(x,x) right? I'm not sure why this is the same as y(x) though??

    Thanks in advance!
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  2. #2
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    There are 2 Leibniz's you have to apply:
    both will generate:
    <br />
\ldots + e^{x-x} y(x) +\ldots - e^{x-x} y(x) + \ldots

    Quickly applied the rule, and found:

    <br />
1+3\int_{0}^{x} e^{3(x-t)} y(t) dt - 3\int_{x}^{1} e^{3(t-x)} y(t) dt<br />

    I might have made a mistake. So be please becareful.

    -O works then hopes.
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