I have a function $f = 4\pi x^2$, where x is a function of $ln(a)$. The problem I am running into is that I need to compute $\frac{\partial}{\frac{\partial x}{\partial ln(a)}}\left(4\pi x^2\right)$.
$\frac{\partial x}{\partial ln(a)}$ is not analytically known, but the goal is to numerically solve coupled 2nd order ODE's. x is one of the variables in the system. How would I approach this? I tried using the chain rule but I always end up with one differential that I cannot do anything with.