I am following a lecture on logistic regression using gradient descent and I have an issuer understanding a short-path for a derivative :
Let be :
- $z=w_1x_1+w_2x_2+b$
- $a=\sigma(z)$
- and the loss function $L(a,y)=-y(\log(a)+(1-y)\log(1-a))$, which I know have a name but I can't remember it it.
In order to have $\frac{\delta\mathcal L(a,y)}{\delta z}$ I am able to compute $\frac{\delta\mathcal L(a,y)}{\delta a}$. But where do we get $\frac{\delta a}{\delta z}=a(1-a)$ ?
I can only have $\frac{\delta a}{\delta z}=\frac{\delta\sigma(w_1x_1+w_2x_2+b)}{\delta z}$