# Math Help - Help on differentiation

1. ## Help on differentiation

$Q(x) = \frac{1}{\sqrt{2 \pi}} \int_x^\infty e^{- t^2/2} dt$

$P = Q( \sqrt{2a \cdot u^2} ) \cdot e^{au^2}$

what is the answer if we differentiate P w.r.t. $u^2$ ???

thanks

2. Originally Posted by graticcio
$Q(x) = \frac{1}{\sqrt{2 \pi}} \int_x^\infty e^{- t^2/2} dt$

$P = Q( \sqrt{2a \cdot u^2} ) \cdot e^{au^2}$

what is the answer if we differentiate P w.r.t. $u^2$ ???

thanks
Put $v=u^2$, then:

$P(v)=Q( \sqrt{2a v} ) ~e^{av}$

$
\frac{d}{dv}P(v)=\frac{\sqrt{2a}}{2\sqrt{v}}~Q'(\s qrt{2a v} ) ~ e^{av}+aP(v)
$

RonL