Skip to main content
Mathematics LibreTexts

3: Rules for Finding Derivatives

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    It is tedious to compute a limit every time we need to know the derivative of a function. Fortunately, we can develop a small collection of examples and rules that allow us to compute the derivative of almost any function we are likely to encounter. Many functions involve quantities raised to a constant power, such as polynomials and more complicated combinations like \(y=(\sin x)^4\). So we start by examining powers of a single variable; this gives us a building block for more complicated examples.

    • 3.1: The Power Rule
      The power rule addresses the derivative of a power function.
    • 3.2: Linearity of the Derivative
      The derivative is a linear operation and behaves "nicely'' with respect to changing its argument function via multiplication by a constant and addition .
    • 3.3: The Product Rule
      The product rule is used to construct the derivative of a product of two functions.
    • 3.4: The Quotient Rule
      The quotient rule use used to compute the derivative of f(x)/g(x) if we already know f′(x) and g′(x).  It is often possible to calculate derivatives in more than one way, as we have already seen. Since every quotient can be written as a product, it is always possible to use the product rule to compute the derivative, though it is not always simpler.
    • 3.5: The Chain Rule
      When simple functions are made into more complicated functions (e.g., composite functions), the chain rule can be used to identify the relevant derivative.
    • 3.E: Rules for Finding Derivatives (Exercises)
      These are homework exercises to accompany David Guichard's "General Calculus" Textmap.

    This page titled 3: Rules for Finding Derivatives is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by David Guichard.

    • Was this article helpful?