Question

高数,高阶导数.已知dx/dy=1/y' 导出d^2x/dy^2=-y''/(y')^3

Answer 1

设 y=f(x) 的反函数为 x=g(y),已知

g'(y) = 1/f'(x),

则

g"(y) = (d/dy)g'(y)

= (d/dx)[1/f'(x)]*(dx/dy)

= {-f'(x)/[f"(x)]^2}*[1/f'(x)]

= -f'(x)/[f"(x)]^3,

就是.