1. Not finding help here? Sign up for a free 30min 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!

Proof of the Quotient Rule

  1. Dec 28, 2009 #1
    1. The problem statement, all variables and given/known data
    if p(x) = f(x)/g(x)

    Prove that

    p'(x) = g(x) f '(x) - f(x) g '(x) / g(x)ˆ2

    2. Relevant equations



    3. The attempt at a solution

    The proof goes like this in my book

    p(x + h) - p(x) / h = [ f(x+h)/ g(x+h) - f(x) / g(x) ] / h

    = f(x + h) g(x) - f(x) g(x + h) / h g(x) g(x + h)



    I dont understand why did g(x) and g(x + h) appeared in the numerator on the last part of the proof? Since g(x) and g(x +h) were already multiplyed by h in the denominator.

    Thanks in advance.
     
  2. jcsd
  3. Dec 28, 2009 #2
    It's just subtracting fractions:

    a/b-c/d = (ad-cb)/d

    a=f(x+h)
    b=g(x+h)

    c=f(x)
    d=g(x)
     
  4. Dec 28, 2009 #3
    By the way... don't leave out the "lim h-->0" when you write out the proof!
     
  5. Dec 28, 2009 #4
    Here is a good write up of the proof with reasons for each step.

    http://people.hofstra.edu/Stefan_waner/RealWorld/proofs/quotientruleproof.html [Broken]
     
    Last edited by a moderator: May 4, 2017
  6. Dec 28, 2009 #5
    Alternatively,

    f(x)/g(x) = f(x)[g(x)]-1.

    Solve by applying the product rule, and the power rule.
     
  7. Dec 28, 2009 #6
    thanks a lot ...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof of the Quotient Rule
  1. Quotient Rule (Replies: 1)

  2. Quotient rule (Replies: 6)

  3. Quotient Rule (Replies: 14)

Loading...