Question

这道题怎么做?跪求 导数方面的设f(x)二阶可导,求y=f(x^2)的二阶导数

Answer 1

y = f(x^2)

令：u = x^2uy = f(x^2) = f(u)

y' = dy/dx = df/du × du/dx = f ' × 2x

= 2x f ’

y '' = d^2 y/ dx^2 = 2(f ' + x f '')

式中：f ' = df/du = f '(x^2)

f '' = d^2f/du^2 = f ''(x^2)