variation of a final state due to changes in period (where the period is a parameter)

Question

I have a simple ordinary differential equation

$\frac{dx}{dt}=f(x,t,p,T)$

$x(0) = x_0$, $x(T) = x_T$

where $p$ and $T$ are constant parameters. How do I compute $\frac{dx_T}{dT}$ ? Thanks!

NOTE: I know I can compute $\frac{dx_T}{dp}$ integrating the equation $\frac{d}{dt} (\frac{dx}{dp}) = \frac{df}{dx}\frac{dx}{dp}+\frac{df}{dp}$ from $t=0$ to $t=T$.