What is a good way to remember derivatives of certain functions for integration such as in session 40 recitation where we would have to know that the derivative of arctan y is y^2 + 1.

Question

amistre64 · Answer

practice.

amistre64 · Answer

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)

amistre64 · Answer

[arctan(y)]' = 1/(y^2+1)

anonymous · Answer

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! :)

anonymous · Answer

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

anonymous · Answer

find the integration and derivatives of such functions by yourself......... i'm sure you don't have to remember then

anonymous · Answer

TI-89 or TI-Nspire cx CAS calculator.

That is all  you'll ever need for doing the rarer trig derivatives ;-)