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Math Help - Finding the derivative of an intergral ...

  1. #1
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    Finding the derivative of an intergral ...

    Hello,

    I am trying to solve the problem below where I am attempting to find the derivative of an intergral. I tried the answer that is typed in but that is incorrect.

    Any ideas? Thanks!



    Regards,
    Chris K.
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  2. #2
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    Try g'(x) = 3\left( {\frac{{3x + 2}}<br />
{{3x - 4}}} \right) - 9\left( {\frac{{9x + 2}}<br />
{{9x - 4}}} \right).
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  3. #3
    Super Member General's Avatar
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    Quote Originally Posted by ckoeber View Post
    Hello,

    I am trying to solve the problem below where I am attempting to find the derivative of an intergral. I tried the answer that is typed in but that is incorrect.

    Any ideas? Thanks!



    Regards,
    Chris K.
    No need for this hint, Just apply the following formula:
    If g(x)=\int_{m(x)}^{h(x)} f(u) du where m and h are differentiable functions.
    then: g'(x) = f(h(x)) h'(x) - f(m(x))m'(x).

    In your question:
    f(u)=\frac{u+2}{u-4}.
    h(x)=3x.
    m(x)=9x.
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  4. #4
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    Quote Originally Posted by General View Post
    No need for this hint, Just apply the following formula:
    If g(x)=\int_{m(x)}^{h(x)} f(u) du where m and h are differentiable functions.
    then: g'(x) = f(h(x)) h'(x) - f(m(x))m'(x).

    In your question:
    f(u)=\frac{u+2}{u-4}.
    h(x)=3x.
    m(x)=9x.
    Thanks! This formula is awesome. Way better than the hint as I was my brain for 2 hours over this.

    I got this:



    Regards,
    Chris K.
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