The derivate of $\tan x$ is very simple obtainable by productrule and can be presented in two forms
$$\frac{d}{dx}\tan x=\frac{1}{\cos^2x}=1+\tan^2x$$
However, i've asked myself has any of these two forms any advantage over the other. (Im asking because i write my own differential-function)
Both can be easily converted into another but thats not the question here.
Both have an comparable easy way to differentiate again and do not build simpler/more complex forms
$\frac{d^2}{dx^2}\tan x=2\frac{\tan x}{\cos^2x}=2\tan(x)\cdot(1+\tan^2x)$
So does any of the two do have have an advantage or something which makes it more appropriate for a transformation, a calculation or something like that which would not be that obvious in the other form?
Perhaps this question was answered before by many CAS-products. Mathematica uses $\dfrac{1}{\cos^2x}=\sec^2x$ probably because its the most readable. What does Maple do and any other CAS you have? (I only have access to Mathematica)