derivative $\displaystyle \int_{0}^{\sqrt{x}} e^{-t^2} $

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- Aug 30th 2009, 12:18 PMpeteryellowdifferentiation
derivative $\displaystyle \int_{0}^{\sqrt{x}} e^{-t^2} $

- Aug 30th 2009, 01:30 PMskeeter
- Aug 30th 2009, 09:35 PMpeteryellow
how is this true?

$\displaystyle

\frac{d}{dx} \left[ \int_a^u f(t) dt\right] = f(u) \cdot \frac{du}{dx}

$? - Aug 30th 2009, 09:55 PMeXist
$\displaystyle \frac{d}{dx}\int_{0}^{\sqrt{x}} e^{-t^2} =

e^{-(\sqrt{x})^2} \frac{d}{dx}(\sqrt{x} - 0) = ?

$

Can you finish it? - Aug 31st 2009, 04:43 AMmr fantastic