It is given the following minimizer:
$$\min(f,b) = \frac a 2 \cdot \| w \|^2 - \sum_{c=1}^C \log \ell(y^c(w^T \cdot x^c + b)), \text{ with } \ell(u) = \frac 1 {1+e^{-u}} $$
I am only interested in the derivation of the log, because it is confusing me. I mean what I have to do now?
Edit:
I guess it is just:
$$ \frac {\partial f(w,b)}{\partial w} = w - \sum (1 + e^{-u}) \cdot g(x)\cdot(1-g(x))$$
$g(x)\cdot(1-g(x))$ found here