List of Derivatives of the basic functions:
All these can be derived using The first principle. However, we do need to get (very) familiar with these.
To learn the basic derivatives, Practice as many questions as you can. First, do the questions referring to the table here & then without it.
Try out various derivative problems to get maximum exposure. You don’t know what to expect when you are sitting in an exam. So, make sure you know how to perform implicit differentiation and explicit differentiation. Most importantly, you should know how to take the second derivative?
While you are practicing to differentiate functions with respect to some variable x or y, use a derivative calculator to verify your answers