推導 Chain Rule
Show d/dx f(g(x)) = (df/dg) (dg/dx)
Proof
d/dx f( g(x) ) = limΔx→0 [ f(g(x+Δx)) - f(g(x)) ] / Δx 其中 f(g(x+Δx)) = f( g(x) + g'(x)Δx + O((Δx)2) ) ~ f( g(x) ) + f'(g(x))(g'(x)Δx) + O( [g'(x)Δx]2)
d/dx f( g(x) ) = limΔx→0 [ f(g(x+Δx)) - f(g(x)) ] / Δx
其中 f(g(x+Δx)) = f( g(x) + g'(x)Δx + O((Δx)2) ) ~ f( g(x) ) + f'(g(x))(g'(x)Δx) + O( [g'(x)Δx]2)