求y=x^3/(x^2-3x-4)的高阶导数y(n)

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求y=x^3/(x^2-3x-4)的高阶导数y(n)
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求y=x^3/(x^2-3x-4)的高阶导数y(n)
求y=x^3/(x^2-3x-4)的高阶导数y(n)

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)
接着再套求导公式即可!