y=x/(x^2-3x+2),求y的n阶导数,
问题描述：
y=x/(x^2-3x+2),求y的n阶导数,
答
y=x/(x^2-3x+2)=2/(x-2) -1/(x-1)故y的n阶导数就等于2/(x-2)与1/(x-1)的n阶导数之差,而[2/(x-2)]′= -2(x-2)^(-2)[2/(x-2)]′′=2*(-1)*(-2)*(x-2)^(-3)[2/(x-2)]′′′=2*(-1)*(-2)*(-3)*(x-2)^(-4).[2/(x-2)]^n=2*...不好意思指出一下，第二行是否为=2x/(x-2)-x(x-1)当然不是的呢，x/(x^2-3x+2)=2/(x-2) -1/(x-1)而2x/(x-2)- x/(x-1)=x^2 /(x^2-3x+2)