先进行有理分式分
f(x)=(4x^2+2x-1)/(2x^2+x-1)
=2 + 1/(2x^2+x-1)
=2 + 1/[(x+1)(2x-1)]
=2 + 1/(x+1) + 1/(x-1/2)
=2 + (x+1)^(-1) + (x-1/2)^(-1)
因此:
f^(n)(x)
=(-1)^n * n!* [ (x+1)^(-n-1) + (x-1/2)^(-n-1) ]
先进行有理分式分
f(x)=(4x^2+2x-1)/(2x^2+x-1)
=2 + 1/(2x^2+x-1)
=2 + 1/[(x+1)(2x-1)]
=2 + 1/(x+1) + 1/(x-1/2)
=2 + (x+1)^(-1) + (x-1/2)^(-1)
因此:
f^(n)(x)
=(-1)^n * n!* [ (x+1)^(-n-1) + (x-1/2)^(-n-1) ]