Backward pass
Working from the loss back to the inputs, multiplying local derivatives to get the gradient of the loss at every node. (When a value feeds several nodes, the gradients coming back along each path are added.)
L depends on w through a chain, w → u → ŷ → e → L, so the chain rule multiplies the local derivatives along it: ∂L/∂w = ∂L/∂e · ∂e/∂ŷ · ∂ŷ/∂u · ∂u/∂w = 2e · 1 · 1 · x (We write ∂ because L depends on several inputs and we change one at a time: a partial derivative.) The backward pass works this out from the end.
See it in action
Try backward pass hands-on in the lesson The chain rule, part of the The maths behind AI course.