Question

f(x)能直接求导吗?下面这类题该怎样做?

Answer 1

是错的,应该是：

y' = dy/dx = [f(x^2)]' =f'(x^2)*(x^2)' = f'(x^2)*(2x) = 2xf'(x^2),

y" = (d/dx)(dy/dx) = [2xf'(x^2)]'

= (2x)'f'(x^2) + (2x)[f'(x^2)]'*(x^2)'

= 2f'(x^2) + (2x)f"(x^2)*(2x)

= 2f'(x^2) + 4(x^2)f"(x^2).