Question

参数方程求导公式二阶

参数方程二阶导数
如何理解参数方程的二阶求导公式：d2y/dx2=d(dy/dx)/dx=d[£'(t)/§'(t))]*dt/dx

Answer 1

x = x(t),y = y(t) => dy/dx = y'(t) / x'(t)记 y'(t)/x'(t) = z(t),考虑新的参量函数 x = x(t),z = z(t) 则 dz/dx = z'(t) / x'(t) 即 d²y/dx² = dz/dx = (dz/dt) * (dt/dx) 即证.