differentiation

**peteryellow** · August 30th 2009, 12:18 PM

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

**skeeter** · August 30th 2009, 01:30 PM

Originally Posted by peteryellow

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 ...

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

**peteryellow** · August 30th 2009, 09:35 PM

how is this true?

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

**eXist** · August 30th 2009, 09:55 PM

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

Can you finish it?

**mr fantastic** · August 31st 2009, 04:43 AM

Originally Posted by peteryellow

how is this true?

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

It follows directly from the chain rule.

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