Special Case Derivatives Overview

Special case derivatives I liken to learning your multiplication tables. Just like you needed to memorize your multiplication tables, these are derivative rules that you just have to memorize. If you have them memorized, then the problems are usually quick to complete. If you don’t have them memorized, the odds of you getting the problem accomplished are slim to none.

One very common theme of all these special case derivatives is that the base case just follows the base derivative rule. However, as soon as the equation gets more complicated than the base case, you will most likely have to apply the Chain Rule. As the more complicated equation is usually something inside that base case.

The other reason that getting these special cases memorized is so important has to do with what happens towards the end of the AP Calculus class. At the end of your AP Calc course, you will learn to do anti-derivatives, which means undoing derivatives. So, in the future you will need to go both directions with these special cases. Meaning starting from the original equation $f\left(x\right)$,  and going to the derivative $f\prime \left(x\right)$, and then starting from the derivative $f\prime \left(x\right)$, and getting back to the original equation $f\left(x\right)$.