Partial derviative of prediction (sigmoid applied) with respect to weight I am very confused as to where a seemingly "extra" term is included in the above mentioned calculation in my Udacity course.  



The above is taking the derivative of a sigmoid so why isn't it just 

$$=\sigma(Wx+b)(1-\sigma(Wx+b)$$
but rather has $\frac{\partial}{\partial w_j}(Wx+b)$ tacked on the tail?
Recall that for chain rule, we have $$\frac{d}{dw}h(g(w))=h'(g(w))g'(w)$$

For the context of your question, $h(t)=\sigma(t)$ and $g(w)=Wx+b$,

hence that is why we have one more term.