Hello @Thrasso00,
Thanks for sharing your work. We can differentiate the following 3 equations separately
l = -y\log{p} - (1-y)\log{(1-p)}
p = \frac{1}{1+\exp{(-z)}}
z = wx
because \frac{\partial{l}}{\partial{w}} = \frac{\partial{l}}{\partial{p}} \frac{\partial{p}}{\partial{z}} \frac{\partial{z}}{\partial{w}}
This should make things easier.
Raymond