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    hello,

    so i know that if i differentiate w.r.t. x {integral of f(x) dx} i get f(x)

    but what do i get

    if i differentiate w.r.t. x {integral from a to b of f(x) dx}

    or

    if i differentiate w.r.t. x {integral from v(x) to u(x) of f(x) dx}

    ?????????????
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    Are you talking about the differentiation involved in C3?
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    no, i'm just self studying, reading a book from Mary L. Boas
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    (Original post by pepsigirl)
    hello,

    so i know that if i differentiate w.r.t. x {integral of f(x) dx} i get f(x)

    but what do i get

    if i differentiate w.r.t. x {integral from a to b of f(x) dx}
    0. The integral is just a constant, after all.

    if i differentiate w.r.t. x {integral from v(x) to u(x) of f(x) dx}
    Suppose F(x) = \int_0^x f(t) dt. Then F'(x) = f(x). Now, use the chain rule to solve your actual problem.
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    (Original post by pepsigirl)
    hello,

    so i know that if i differentiate w.r.t. x {integral of f(x) dx} i get f(x)

    but what do i get

    if i differentiate w.r.t. x {integral from a to b of f(x) dx}

    or

    if i differentiate w.r.t. x {integral from v(x) to u(x) of f(x) dx}

    ?????????????
    For your first question, the integral from a to b of f(x) dx would be a constant. Therefore, the derivative of that would simply be zero.

    For your second question, the answer would be

    f(u(x))*u'(x) - f(v(x))*v'(x)

    And also, if you're given a mixed type of problem (with a constant and a function), the same rules apply.

    For example, differentiate w.r.t. x {integral from A to U(x) of f(x) dx} would be 0 - f(U(x))*U'(x)
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    i 've looked up this rule called Leibniz's rule it says

    d/dx of integral from u(x) to v(x) of f(x,t) dt =

    f(x,v) (dv/dx) - f(x,u) (du/dx)
    +integral from u(x) to v(x) of partial derivative of f w.r.t. x dt

    and so with regard your answer i don't understand this last bit, b/c in the case of

    d/dx of integral from u(x) to v(x) of f(x) dx =

    f(v) v'(x) - f(u) u'(x) PLUS
    integral from u(x) to v() of partial deriv. of f(x) w.r.t x dx

    ?????
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    it must be something really obvious and i just can't see it i know... but i cant
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    (Original post by pepsigirl)
    i 've looked up this rule called Leibniz's rule it says

    d/dx of integral from u(x) to v(x) of f(x,t) dt =

    f(x,v) (dv/dx) - f(x,u) (du/dx)
    +integral from u(x) to v(x) of partial derivative of f w.r.t. x dt

    and so with regard your answer i don't understand this last bit, b/c in the case of

    d/dx of integral from u(x) to v(x) of f(x) dx =

    f(v) v'(x) - f(u) u'(x) PLUS
    integral from u(x) to v() of partial deriv. of f(x) w.r.t x dx

    ?????
    I can't that I know anything about Leibniz's rule; however, from looking at your example and from the wikipedia article, I think that in our cases, discussed above, f(x,t) is only a function of one variable (f(x) or f(t) depending on whether we have dx or dt).

    In that case, I believe that makes the second part of the equation "the PLUS" part tend to zero and thus can be ignored.

    EDIT: Looking at it more, I think that if you define f(x,t) as a function of one variable, then the last part of it - that whole complicated partial part - would be a function of 'x' or 't' while the partial derivative would be of the opposite value, 't' or 'x' respectively, and therefore would be zero - which means the integral would be zero (regardless of the limits).
 
 
 
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