Question

复合函数求导公式推导

Answer 1

F'(g(x)) = [ F(g(x+dx)) - F(g(x)) ] / dx .(1)

g(x+dx) - g(x) = g'(x)*dx = dg(x) .(2)

g(x+dx) = g(x) + dg(x) .(3)

F'(g(x)) = [ F(g(x) + dg(x)) - F(g(x)) ] /dx =

[ F(g(x) + dg(x)) - F(g(x)) ] / dg(x) * dg(x)/dx =

F'(g) * g'(x)