There are some important rules to remember when computing the derivative of functions. The first is the sum rule:

where a and b are real numbers, f and g are functions, and (’) is the derivative operator. The next is the product rule:

As a corollary to the product rule, the following is also true:

where a is a constant. This rule follows from the product rule because the derivative of a constant is 0 (the slope of the function f(x) = a is 0 for all x). The next rule is the quotient rule:

Finally, there is the chain rule. The chain rule dictates how the derivative is determined when the function f is written in terms of another function: f = f(k) where k = k(x):

The derivatives of some common functions are listed below. Using these given derivatives and the derivative rules listed above, the derivatives of a great many more complicated functions can be determined. Derivatives of other basic functions are available in the appendices of most calculus texts.