For a research problem in reaction engineering I have to numerically calculate what's called the "Degree of Rate Control" defined as follows:
$$DRC=\frac{\partial}{\partial k^+}\ln{s}|_K$$
the derivative of a quantity called $s$ (a function of $k^+$ and $k^-$, so $s(k^+,k^-)$) with respect to $k^+$ while keeping the ratio $K = \frac{k^+}{k^-}$ constant. Since this is not what I usually know as a partial derivative (since $k^-$ is not held constant), it would be quiet tedious for me to achieve with e.g. finite differencing and since I can easily calculate both
$$\frac{\partial}{\partial k^+}\ln{s}|_{k^-}$$
and
$$\frac{\partial}{\partial k^-}\ln{s}|_{k^+}$$
I was wondering if there is a way to calculate these quantities on its own and afterwards calculate the $DRC$ from these two reults. I honestly don't know if it is possible and I will happily take a "no" as an answer ( although a "yes" would make me even happier).
Thanks for your help!