Labs

Calculus · A small change, twice

Chain rule, two maps

x → u → y. See du and dy from dx. Backprop is this picture with more names.

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u = x²dxdu→y = sin ududy
du/dx = 2x
1.60
dy/du = cos u
0.80
dy/dx = product
1.28
dx 0.25 → du 0.400 → dy 0.321

2x = 1.6 and cos u = 0.80. The two slopes multiply: 1.28.

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Chain rule, two maps

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