1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is the quotient rule

  1. Jul 23, 2014 #1
    Definition/Summary

    The quotient rule is a formula for the derivative of the quotient of two functions, for which derivatives exist.

    Equations

    [tex]f(x) = \frac{g(x)}{h(x)}[/tex]

    Then,

    [tex]f'(x) = \frac{h(x)g'(x)-g(x)h'(x)}{(h(x))^2}[/tex]

    here, [itex]h(x) \: \neq \: 0[/itex]

    Extended explanation

    Even though a quotient can always be differentiated using the product and chain rules, it is easier and more efficient to remember and use the quotient rule. :wink:

    Proof of the quotient rule:
    [tex]f(x) = \frac{g(x)}{h(x)} = g(x)[h(x)]^{-1}[/tex]
    Using the product and chain rules:
    [tex]f'(x) = g'(x)\:[h(x)]^{-1} - \: [h(x)]^{-2} \: h'(x)\:g(x)[/tex]
    and, putting this over a common denominator:
    [tex]f'(x) = \frac{h(x)g'(x)-g(x)h'(x)}{(h(x))^2}[/tex]

    * This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: What is the quotient rule
  1. What is quotient? (Replies: 3)

  2. Quotient Rule (Replies: 6)

Loading...