Introduction to Differentiation Rules

What you’ll learn to do: Apply the differentiation rules to determine a derivative

Finding derivatives of functions by using the definition of the derivative can be a lengthy and, for certain functions, a rather challenging process. For example, previously we found that ddx(x)=12x by using a process that involved multiplying an expression by a conjugate prior to evaluating a limit. The process that we could use to evaluate ddx(x3) using the definition, while similar, is more complicated. In this section, we develop rules for finding derivatives that allow us to bypass this process. We begin with the basics.