Memorization

This is a post based on a question.

I'm going to sixth grade and I still haven't memorized my multiplication tables. Help me?

This is more of a series of helpful hints than an actual lesson.
While the vast majority (and most exciting parts) of math involves critical thinking, problem solving, and multi-step processes, there are certain parts that just require some simple memorization. For example, once you have the concept of what multiplication actually is, it is immensely helpful (perhaps even necessary) to simply memorize multiplication tables for all combinations of numbers 0-12. Likewise, in Calculus it can greatly improve your test-taking speed by just memorizing certain basic derivatives and antiderivatives.

Before I go any further, I must make an extremely important point: the goal of memorization is not to substitute for understanding, but to increase mental speed. That is, you should know what I mean when I ask what 4x6 is, and not just know the answer. You must first deeply understand the concepts before memorizing the numbers.

I have a few tried-and-true methods for memorizing simple facts, such as times tables and derivatives. It is best to try all of them and see which works best for you. Everyone's mind works differently and there are numerous learning styles to take into account when selecting a method.

The Power Rule

This is a calculus lesson based on a question:

 Would you be able to explain how to derive a square root? 

The power rule is used to find the derivative of (or "differentiate" or "find the instantaneous rate of change of") an algebraic expression of the form x to a numerical power, or xⁿ.

The derivative of a function ƒ(x) = xⁿ is ƒ'(x) = n * x^n-1. If it is easier to remember think of it as dragging the exponent down (to multiply the x by) and then subtracting one in the exponent.

Here are some examples to clarify: