I have the following equation,
$$ K_r=\left ( \frac{P}{RT} \right )^{v}exp \left \{ \sum_{s}\left [ (\beta_{s,r}-\alpha_{s,r}) \left \langle \frac{h_s}{RT}-\frac{s_s}{R}\right \rangle \right ] \right \} $$
where $$ v=\sum_{s}\left(\beta_{s,r}-\alpha_{s,r}\right) $$ $$ \frac{h_s}{RT}=-\frac{a_1}{T^2}+a_2\frac{ln(T)}{T}+a_3+a_4\frac{T}{2}+a_5\frac{T^2}{3}+a_6\frac{T^3}{4}+a_7\frac{T^4}{5}+\frac{a_8}{T} $$ $$ \frac{s_s}{R}=-\frac{a_1}{2T^2}-\frac{a_2}{T}+a_3ln(T)+a_4T+a_5\frac{T^2}{2}+a_6\frac{T^3}{3}+a_7\frac{T^4}{4}+a_9 $$
R, P, $a_1$ to $a_9$, $\beta$ and $\alpha$ are constants.
I am interested in obtaining $$ \frac{\mathrm{d} K_r}{\mathrm{d} T} $$ But I don't know how to proceed. how do I derive a summation inside an exponential?
Thanks for your help.