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Math Help - find the derivative

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    find the derivative



    h'(x)=
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    H(x) = \int_c^{f(x)} {G(t)dt} \, \Rightarrow \,H'(x) = G\left( {f(x)} \right)f'(x)
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    i cant get it could use some more help
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    Quote Originally Posted by dat1611 View Post
    i cant get it could use some more help
    \frac{d}{dx}\left[\int_a^u f(t) \, dt \right] = f(u) \cdot \frac{du}{dx}

    substitute u = \sin{x} in for t in the integrand, then multiply that result by the derivative of \sin{x}.
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  5. #5
    Senior Member Twig's Avatar
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    Hi!

    Let  u = sin(x)

    h(u)=\int_{-5}^{u} (cos(t^{3})+t) \; dt

    \frac{dh}{dx}=\frac{dh}{du} \cdot \frac{du}{dx}

    h'(x)=(cos(sin^{3}(x))+sin(x))\cdot cos(x)
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