1/(1-\(x^{2}\))
=1/(1+x)(1-x)
=(\(\frac{1}{2}\)){1/(1+x)+1/(1-x)}
=(\(\frac{1}{2}\)){1/(1+x)-1/(x-1)}

よってn次導関数は

(\(\frac{1}{2}\))(n!)(-1\()^{n}\){1/(1+x)^(n+1)-1/(x-1)^(n+1)}