where does the following identity come from?

Question

I was given the following identity:

$\partial w_{ki} f(w_{ki}) =f(w_{ki}) \cdot \partial w_{ki}log(f(w_{ki}))$

and I'm wondering where this actually comes from, because I can't relate it to anything I've seen before!

mikey

Answer 1

The notation is a little strange, but if I understand it correctly, since $$ \frac{d}{dx} \log(f(x)) = \frac{f'(x)}{f(x)} $$ we have $$ f'(x) = f(x) \frac{d}{dx} \log(f(x)). $$ (Yours is the same, but the derivatives are partial derivatives with respect to $w_{ki}$.)