Which form is more ethical for the given derivative?

Question

So I'm asked to find the derivative of $F(x)=\tan^{-1}(\frac{1+x}{1-x})$, and I arrive at the answer of $F'(x)=\frac{2}{2+2x^2}$, however my college mates argue that $F'(x)=\frac{2}{(1-x)^2+(1+x)^2}$ should be the simplest form. What should be the standards of what we call the "simplest form" be? my assumption is that it has to be in the lowest degree I can get it, and with less independent variables.

Answer 1

The question is not which form is the simpler. The question is, which form is the more useful. And the answer to that question is, it depends. It depends on what you're going to do with the formula. If you are going to use it in some further calculations, then you can try the one expression, and try the other, and see which one makes the further calculations the easiest. But if you're not going to do anything with the formula, if just getting the derivative is all you want to do, then I can't see much reason for preferring either one to the other. And, as Kavi wrote in the comments, "ethics" has nothing to do with it. Maybe you meant "aesthetics", but that's in the eye of the beholder.