求y=x^3/(x^2-3x-4)的高阶导数y(n)

问题描述:

求y=x^3/(x^2-3x-4)的高阶导数y(n)

y=x^3/(x^2-3x-4)=x^3/(x+1)(x-4)=(x^3+1-1)/(x+1)(x-4)=(x^2+x+1)/(x-4)-1/(x+1)(x-4)=(x^2-4x+5x-20+21)/(x-4)-1/5[1/(x-4)-1/(x+1)]=x+5+21/(x-4)-1/5[1/(x-4)-1/(x+1)]=x+5+104/5*1/(x-4)+1/5*1/(x+1)接着再套求...