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!

Homework Help: Need help with quotient rule

  1. Jan 11, 2012 #1
    1. The problem statement, all variables and given/known data

    I want to prove that if [tex] y = \frac{u}{v} [/tex]

    then [tex] \frac{dy}{dx} = \frac{ v \frac{du}{dx} - u \frac{dv}{dx} }{v²} [/tex]

    u and v are functions of x.

    2. The attempt at a solution

    [tex] y = uv^{-1} [/tex]

    [tex] y + dy = ( u + du ) ( v + dv )^{-1} [/tex]

    then I suppose I could use Newton's Binomial to develop

    [tex] ( v + dv )^{-1} [/tex]

    but I don't know how to use the formula

    [tex] (a+b)^{n} = \sum_{k=0}^{n} \dbinom{n}{k} a^{n-k} b^k [/tex]

    with a negative exponent. I'm familiar with binomial coefficients but that negative exponent is leaving me without a clue.

    Any help would be very much appreciated, thank you!
    Last edited: Jan 11, 2012
  2. jcsd
  3. Jan 11, 2012 #2

    Char. Limit

    User Avatar
    Gold Member

    That seems like a rather awkward way to do it. Are you allowed to use the product rule in your proof?
  4. Jan 11, 2012 #3
    I am learning by myself for now, so I'm pretty much allowed to use anything.
    How would you do it using the product rule?
  5. Jan 11, 2012 #4

    Char. Limit

    User Avatar
    Gold Member

    Well, if you can use the product rule, it becomes a lot easier. Since the product rule is:

    (uv)' = u v' + u' v

    Just say (u * 1/v)' = u (1/v)' + u' (1/v)

    and solve from there.
  6. Jan 11, 2012 #5
    Oooh this is indeed much simpler. Thank you!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook