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Math Help - differentiation

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    differentiation

    derivative \int_{0}^{\sqrt{x}} e^{-t^2}
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    Quote Originally Posted by peteryellow View Post
    derivative \int_{0}^{\sqrt{x}} e^{-t^2}
    this is the second question you've asked regarding this topic. note that u is a function of x ...

    \frac{d}{dx} \left[ \int_a^u f(t) dt\right] = f(u) \cdot \frac{du}{dx}
    Last edited by mr fantastic; August 30th 2009 at 08:12 PM.
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    how is this true?

    <br /> <br />
\frac{d}{dx} \left[ \int_a^u f(t) dt\right] = f(u) \cdot \frac{du}{dx}<br />
?
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  4. #4
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    \frac{d}{dx}\int_{0}^{\sqrt{x}} e^{-t^2} =<br />
e^{-(\sqrt{x})^2} \frac{d}{dx}(\sqrt{x} - 0) = ?<br />

    Can you finish it?
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  5. #5
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    Quote Originally Posted by peteryellow View Post
    how is this true?

    <br /> <br />
\frac{d}{dx} \left[ \int_a^u f(t) dt\right] = f(u) \cdot \frac{du}{dx}<br />
?
    It follows directly from the chain rule.
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