Derivative Rules

There are many rules that can be used to find the derivative of a function. These are quick rules that can be proved using the limit definition of the derivative, but once you know the rules you can use them to save time when finding the derivative. The six basic rules we looked at are shown below. These rules assume that c is a constant, u and v are functions in terms of x, and that the derivative exists for all x's in the domain of the function.



You must also be able to read the notation in the book. Below is a brief list of the notation that your book and many other mathematical texts use to identify the first-order derivative and its successors.



In the next sections, we will introduce more rules that will help us find the derivatives of trigonometric, logarithmic, and exponential functions.