d^2y/dx^2x^2不应用括号括住吗?dx*dx与d（x^2）为什么相同f(x^2)的二阶导数d^2y/dx^2,

Question

d^2y/dx^2 x^2不应用括号括住吗?dx*dx与d（x^2）为什么相同
f(x^2)的二阶导数d^2y/dx^2,

Answer 1

d²y/dx² = d(dy/dx) / dx
dx*dx = (dx)², d(x²) = 2x dx
令 g(x) = f(x²) = f(u), u =x²
g '(x) = f '(u) * du/dx = 2x f '(u)
g ''(x) = 2 f '(u) + 2x * f ''(u) * du/dx
= 2 f '(u) + 2x * f ''(u) * 2x
= 2 f '(x²) + 4x² * f ''(x²)