[Math] Divide first derivative with initial function

Question

Say we have function $f(x)$ and its first derivative $f'(x)$. What do we get when we take $\frac{f'(x)}{f(x)}$ ?

I see this a lot in the mathematics of economic models, but I don't quite get the intuition behind such an operation.

Thanks!

Answer 1

The quantity $\frac{f'(x)}{f(x)}\times100$ gives the percentage change for $f(x)$ You can relate it to the usual percentage change calculations, which is similar to $\frac{\Delta N}{N}\times 100$