To start learning how to calculate function derivatives (the real ones, not from the definition), you should of course start by preparing a sheet with formulas.
Tip
An important thing then is to use it at every step, during every exact transition. Absolutely do not calculate anything by heart, nor “by feel”. Don’t rush. Don’t abbreviate. Don’t try to memorize patterns especially by heart. Use only the sheet. Every step should be justified by a derivative formula from the sheet. Time for quick memorization calculations will come later.
I explain in more detail what I mean in the first solved examples in my Video Course on derivatives (Lesson 2). You can best verify the accuracy of the steps you input using our mathematical app for calculating derivatives.
Good luck!