设y=f(1/x),其中f(u)为二阶可导函数,则d^2y/dx^2=?

Question

设y=f(1/x),其中f(u)为二阶可导函数,则d^2y/dx^2=?

Answer 1

dy/dx=f'(1/x)*(-1/x^2)
d^2y/dx^2=f''(1/x)*(-1/x^2)(-1/x^2)+f'(1/x)*(2/x^3)
=f''(1/x)/x^4+2f'(1/x)/x^3