It is tedious to compute a limit every time we need to know the derivative of a function. Fortunately, we can develop a small collection of examples and rules that allow us to compute the derivative of almost any function we are likely to encounter. Many functions involve quantities raised to a constant power, such as polynomials and more complicated combinations like $y=(\sin x)^4$. So we start by examining powers of a single variable; this gives us a building block for more complicated examples.

1. The Power Rule

2. Linearity of the Derivative

3. The Product Rule

4. The Quotient Rule

5. The Chain Rule