I'm trying this:

$\displaystyle

P(x)=\int_{-\infty}^{x} \frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{t^2}{2\sigma^2}} dt

$

which is just the gaussian function with $\displaystyle \mu=0 $.

I wanna get:

$\displaystyle

\frac{\partial F}{\partial \sigma}=?

$

Any ideas?