Each weight gradient is the upstream gradient times the input feeding that weight. This lesson names those derivatives parameter by parameter, so each exact fraction is tied to the weight it describes. The branch with zero upstream gradient contributes exact zeroes, not approximate small values.
highlighted = computed this step
First hidden-unit gradients
For the first hidden unit, dL/dz1=-2. Multiplying by x1 and x2 gives dL/dw11=-2 and dL/dw12=-4. Each one is the exact derivative for that named weight: upstream pre-activation gradient times the local input.
dw11dL=−2⋅1=−2,dw12dL=−2⋅2=−4
Biases and the blocked unit
The first bias gradient is dL/db1=-2. Since dL/dz2=0, the second hidden unit has zero weight and bias gradients. A closed ReLU gate upstream makes every local multiplication on the second branch land at zero.
db1dL=−2,dw21dL=dw22dL=db2dL=0
Summary
The parameter-gradient register is exact: dw11=-2, dw12=-4, db1=-2, and the dead branch entries are all 0. The table is the chain rule applied edge by edge to the exact forward graph.