Results 1 to 6 of 6

Math Help - Quotient Rule Problem

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    32

    Quotient Rule Problem

    The problem is to use the quotient rule to find the derivation of: f(x) = x / (x + (c/x))

    I keep using the quotient rule over and over again with no success. Am I supposed to separately use the rule on c/x, and then use it on the whole function? Whether I am or not, could you please go through the problem step by step? I keep trying different ways to figure it out; I am unsure whether it is a problem with strategy or with algebra. Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Well, let's see what you are doing?

    Often, it is legal to use a little algebra to make your life easier. Compare your expression to \frac{x^{2}}{x^{2}+c}. It's not quite the same thing, but it may be close enough.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,871
    Thanks
    655
    Quote Originally Posted by Maziana View Post
    The problem is to use the quotient rule to find the derivation of: f(x) = x / (x + (c/x))

    I keep using the quotient rule over and over again with no success. Am I supposed to separately use the rule on c/x, and then use it on the whole function? Whether I am or not, could you please go through the problem step by step? I keep trying different ways to figure it out; I am unsure whether it is a problem with strategy or with algebra. Thanks.
    since x cannot equal 0, multiply numerator and denominator by x ...

    f(x) = \frac{x^2}{x^2+c}

    now use the quotient rule
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2009
    Posts
    32
    Thanks. (Sorry, I don't know how to format mathematical equations on here)

    f'(x) = x^2/(x^2 + c)

    = (x^2 + c)(2x) - (x^2)(2x + 1) / (x^2 + c)^2

    = 2x^3 + 2xc - 2x^3 - x^2 / (x^2 + c)^2

    = (2xc - x^2) / (x^2 + c)^2

    Is that right? Is it the final answer, or is there anything else I can do?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    There's your problem: \frac{d}{dx}(Constant)\;=\;0

    You have: \frac{d}{dx}(c)\;=\;1 -- No good.

    See how quickly we can get to the heart of the problem when the student shows the work?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Sep 2009
    Posts
    32
    You're right; I was thinking of it as a variable. Thanks so much.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. finishing a quotient rule problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 19th 2011, 08:01 AM
  2. Quotient rule differentiation problem..
    Posted in the Calculus Forum
    Replies: 11
    Last Post: April 4th 2010, 09:33 AM
  3. Chain rule / quotient problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 6th 2009, 11:57 AM
  4. Quotient Rule Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 12th 2009, 07:11 AM
  5. Quotient Rule Word Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 1st 2006, 06:35 PM

Search Tags


/mathhelpforum @mathhelpforum