1. differentiation

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

2. 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 ...

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

3. how is this true?

$

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

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

Can you finish it?

5. 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.