core practice · coding problem
Chain rule on a tiny graph
y = (2x+1)³. Compute dy/dx at x=1 via chain rule (u=2x+1, y=u³).
The mechanism
Backpropagation is how the network learns: compute the error at the output, then push that error backwards through each layer using the chain rule from calculus. You reuse values from the forward pass so you do not have to recompute them.
Expected evidence
dy/dx = 6(2x+1)² → 54 at x=1.
Try this drill in the practice workspace →
Hints when you need them
- dy/dx = dy/du · du/dx.
- du/dx = 2.