F′[g(x)]与{f(g(x))}′的区别

Question

F′[g(x)]与{f(g(x))}′的区别

Answer 1

F'(g(x))就是先求出F'(x)后,将其中的x全部替换成g(x).举例：F(x)=x²,则F'(x)=2x,则F'(g(x))=2g(x).
{f[g(x)]}'=f'(x)×g'(x).举例：f(x)=x²,g(x)=2x＋1,则{f[g(x)]}'=2[g(x)]×g'(x)=2[2x＋1]×2=8x＋4