Finding the $N$-th derivative of $f(x)=\frac {x} {x^2-1}$ I'm practicing some problems from past exams and found this one:

Find the n-th derivative of this function:
$$f(x)=\frac {x} {x^2-1}$$


I have no idea how to start solving this problems. Is there any theorem for finding nth derivative?

To add to Derek's hint: you will have to show the validity of the formula
$\frac{\mathrm{d}^k}{\mathrm{d}x^k}\frac1{x}=\frac{(-1)^k k!}{x^{k+1}}$
