(a) Compute the first few derivatives of the function f(x) = 1/ (x2 + x) until you see that the computations are becoming algebraically unmanageable.
(b) Use the identity to compute the derivatives much more easily.

Then find an expression for f(n)(x). This method of splitting up a fraction in terms of simpler fractions, called partial fractions, will be pursued further in Section 7.4.

1 x (x + 1) x +1