← Lesson
The Chain Rule
Joeven
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def g(x): return 3 * x + 1 def f(u): return u * u def y(x): return f(g(x)) x = 2.0 u = g(x) dydx_chain = (2 * u) * 3 h = 1e-5 dydx_num = (y(x + h) - y(x - h)) / (2 * h) print("x", x, "u=g(x)", u, "y", y(x)) print("chain rule dy/dx", dydx_chain) print("nudge dy/dx", dydx_num) w, b = 3.0, 1.0 u = w * x + b y_out = u * u dy_du = 2 * u du_dx = w du_dw = x dy_dx = dy_du * du_dx dy_dw = dy_du * du_dw print("backprop dy/dx", dy_dx, "dy/dw", dy_dw)
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