Question

设f(x)二阶可导,求y=f(x^2)的二阶导数.（麻烦请写出思路和过程.）

Answer 1

f(x²)为复合函数,用复合函数求导法则,外导乘以内导

y'=f'(x²)*(x²)'=2xf'(x²)

y''=2f'(x²)+2xf''(x²)*2x

=2f'(x²)+4x²f''(x²)