Implement backpropagation and gradient descent step

Extend the scratch forward pass to compute gradients for a single hidden-layer network using binary cross-entropy loss. Implement the backward pass (chain rule) and update weights using a basic learning rate. Show the loss decreasing over 10 iterations on a small data batch.

Locate the notebook containing the scratch forward pass and read how the single hidden-layer network and binary cross-entropy loss are represented. Trace the forward-pass values first, then use the issue's chain-rule and weight-update requirements as the scope. Run the notebook on the small batch and verify that the reported loss decreases across 10 iterations.

Written by the indexing model from the issue text.