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.<\/p>","rendered":"
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.<\/p>\n\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t