# Neural Networks: Computing Partial Derivatives

We will compute the partial derivative of the Cross-Entropy cost function

with respect to one weight in each connection with a sigmoid activation function for each layer.

Given

Therefore

Take aways:

- We Can compute the partial derivative of a weight by multiplying the value of the node in layer
**โ**and the ๐ฟ of the connected node in layer**โ**+1 - ๐ฟโs of the nodes in layer
**โ**can be computed from the ๐ฟโs of the nodes in the layer**โ**+1