$d = \frac{(u+au)^2}{\frac{u^2}{r} + \frac{(au)^2}{s}}$
I have a basic question concerning derivatives. If I need to find the max of $d(a)$, I know I need to take derivatives... but with respect to what according to the d(a) notation? All I read that is that I need the max of d evaluated at a
The fact that you specified "d(a)" implies that this is a function of a only, that u and r are constants. Differentiate with respect to a.