# differentiation

• Aug 30th 2009, 12:18 PM
peteryellow
differentiation
derivative $\int_{0}^{\sqrt{x}} e^{-t^2}$
• Aug 30th 2009, 01:30 PM
skeeter
Quote:

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 ...

$\frac{d}{dx} \left[ \int_a^u f(t) dt\right] = f(u) \cdot \frac{du}{dx}$
• Aug 30th 2009, 09:35 PM
peteryellow
how is this true?

$

\frac{d}{dx} \left[ \int_a^u f(t) dt\right] = f(u) \cdot \frac{du}{dx}
$
?
• Aug 30th 2009, 09:55 PM
eXist
$\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 AM
mr fantastic
Quote:

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.