1. The problem statement, all variables and given/known data Show that the fifth derivative of arctan(x) equals (120x^4 - 240x^2 + 24)/((x^2 + 1)^5). Then, calculate the fifth order Taylor series of arctan(x) around x = 0. 2. Relevant equations Differentiation rules; knowing how a Taylor series works. 3. The attempt at a solution I tried the brute-force way of differrentiating those fractions over and over and over again, resulting in one big mess. My answer ultimately turned out to be something different than what was asked, which isn't particularly surprising, considering the number of calculations I had to perform. I didn't even get to the Taylor series part. My question is: is there a non-obvious solution to this problem that I'm missing? If so, could anyone give me a hint? I've been stuck on this problem for over an hour now and I'm not exactly fond of the idea of redoing all my previous calculations.