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Homework Help: 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 ...
     
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