What is the derivative of $Q_m\left(\frac{\alpha}{x^a},\frac{\beta}{x^b}\right)$ with respect to $x$, i.e,

$$\frac{\partial}{\partial x}Q_m\left(\frac{\alpha}{x^a},\frac{\beta}{x^b}\right), \quad \text{ where } \alpha,\beta,a,b \in \mathbb{R} \text{ and } m\in \mathbb{N} $$

where the $Q_m(.,.)$ is a special function( http://en.wikipedia.org/wiki/Marcum_Q-function ) , and we have

$$Q_m\left(\frac{\alpha}{x^a},\frac{\beta}{x^b}\right)= \left(\frac{x^a}{\alpha}\right)^{m-1} \int^\infty_{\frac{\beta}{x^b}} \: t^m \exp\left(-\frac{t^2}{2}-\frac{\alpha^2}{2x^{2a}}\right) I_{m-1}\left(\frac{\alpha}{x^a}t\right) \:\mathrm{d}t$$

where $I_m(.)$ is the modified bessel function of the first kind with order $m $. Please note that the lower limit of the integral is $\displaystyle\frac{\beta}{x^b}$.