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arctan(y) = x
y = tan(x) <---- well come back to this
Dy(y = tan(x)): 1 = sec^2(x) x'
x' = 1/sec^2(x)
sec^2 = tan^2+1 soooo
x' = 1/(tan^2(x)+1); recall that tan(x) = y
x' = 1/(y^2+1)
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I don't think it's much a good idea to just memorize every derivative,you could try and memorize the standard one and derive the rest when required.After sufficient practice you will see that you memory will converge to the right one almost instantly! Good luck! :)
I think the better way to remember, is to do a lot of exercises, so you can think faster but also understand the meaning of the answers. It's not about memorizing
find the integration and derivatives of such functions by yourself......... i'm sure you don't have to remember then
TI-89 or TI-Nspire cx CAS calculator.
That is all you'll ever need for doing the rarer trig derivatives ;-)