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Math Help - Leibniz formula and chain rule

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    5

    Leibniz formula and chain rule

    Hi,

    I've been learning Maths by myself and I got stuck with the Leibniz formula. The theory is as follows:
    "
    Lets suppose that both partial derivatives of f(t,x) exist and that a(t) and b(t) are derivable functions and F (t).

    F (t) = ∫b(t)a(t) f (t, x) dx for all t.
    Then F '(t) = f (t, b(t))b'(t) − f (t, a(t))a'(t) + ∫b(t)a(t) f 1'(t, x) dx.

    So, I donīt completely understand the formula and I got my exercises wrong once and again. Please, could you explain step by step how to do it? I'll write you below and exercise and my attempt to get a) done.

    For example: Find F'(t) in the following examples:
    a) F (t) = ∫2tt x2 [squared x] dx .
    b) F(t)= ∫21 (etx)/x dx
    What I did in a)

    F'(t)= (2t)
    2*2 - (t)2 + ∫2tt 2x dx -->
    -->
    4t2*2 - t2 + ∫2tt 2x dx
    --> 7t2 + (2t)2 - (t)2
    -->
    4t2
    ANSWER IN THE BOOK:
    F'(t)= (2t)2*2 - (t)2 = 7t2

    ANY HELP WOULD BE REALLY APPRECIATED.

    THANK YOU


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  2. #2
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    Please look here
    Differentiation under the integral sign - Wikipedia, the free encyclopedia
    Could you look Latex help in the main window of MHF.
    I can't understand what is written in (a).
    Last edited by zzzoak; September 26th 2010 at 03:27 PM.
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