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 [latex]\frac{d}{dx}(\sqrt{x})=\frac{1}{2\sqrt{x}}[/latex] 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 [latex]\frac{d}{dx}(\sqrt[3]{x})[/latex] 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.