Basic Rules of Differentiation (Part 1)

There are two basic rules that we can consider the "baby steps" to begin learning calculus. These are the derivative of a constant and the derivative of a variable raised to a constant exponent. 

Derivative of Constant:

The derivative of any constant is zero. Consider the following function f(x), where c is any constant.

Derivative of a Variable Raised to a Constant Exponent:

This is the second rule of differentiation that any calculus student must learn. Consider the following function f(x) where a is any real valued exponent.

In this case, we basically bring down the exponent to the front, and then, subtract 1 to the exponent.

Examples:

Now we will have a few examples that show how important these two rules are. Basically, the derivative of any polynomial function can be obtained from just these two rules.

Many real life situations can be described by polynomial functions, so it is safe to say that these two rules of differentiation will be used frequently.