Results 1 to 5 of 5

Math Help - derivative.. problem

  1. #1
    Senior Member
    Joined
    Sep 2009
    Posts
    300

    derivative.. problem

    Hello,
    I have a quotient problem on the photo attached,
    I have gone wrong on some parts involving exponents I think

    I need some kind person to show me how to do it PLEASE

    Attached Thumbnails Attached Thumbnails derivative.. problem-quotient-problem.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2010
    Posts
    354
    I strongly suggest that you rewrite the problem at the beginning to make it easier.

    f(x) ~=~ \frac{x^{-1}-2x^{-2}}{2x^{-3}-3x^{-4}}<br />
~=~ \frac{x^{-1}-2x^{-2}}{2x^{-3}-3x^{-4}} \cdot \frac{x^4}{x^4}<br />
~=~ \frac{x^3-2x^2}{2x-3}

    Now, work from this instead and it should be a lot easier.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602
    Quote Originally Posted by wolfhound View Post
    Hello,
    I have a quotient problem on the photo attached,
    I have gone wrong on some parts involving exponents I think

    I need some kind person to show me how to do it PLEASE

    Are you asking to find the derivative of

    f(x) = \frac{\frac{1}{x} - \frac{2}{x^2}}{\frac{2}{x^3} - \frac{3}{x^4}}?


    f(x) = \frac{\frac{x - 2}{x^2}}{\frac{2x - 3}{x^4}}

     = \frac{x^2(x - 2)}{2x - 3}

     = \frac{x^3 - 2x^2}{2x - 3}.


    So now by using the quotient rule...

    f'(x) = \frac{(2x - 3)(3x^2 - 4x) - 2(x^3 - 2x^2)}{(2x - 3)^2}

     = \frac{6x^3 - 8x^2 - 9x^2 + 12x - 2x^3 + 4x^2}{(2x - 3)^2}

     = \frac{4x^3 + 13x^2 + 12x}{(2x - 3)^2}

     = \frac{x(4x^2 + 13x + 12)}{(2x - 3)^2}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by wolfhound View Post
    Hello,
    I have a quotient problem on the photo attached,
    I have gone wrong on some parts involving exponents I think

    I need some kind person to show me how to do it PLEASE


    Dude, you love to suffer. First, simplify the expression for f(x)(remember: \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}):

    f(x)=\frac{\displaystyle{\frac{1}{x}-\frac{2}{x^2}}}{\displaystyle{\frac{2}{x^3}-\frac{3}{x^4}}}=\frac{\displaystyle{\frac{x-2}{x^2}}}{\displaystyle{\frac{2x-3}{x^4}}} =\frac{x^2(x-2)}{2x-3}=\frac{x^3-2x^2}{2x-3} ,and now you derivate: much simpler.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Sep 2009
    Posts
    300


    Thanks for the help everyone
    excellent!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 28th 2010, 09:37 PM
  2. Derivative Problem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 27th 2010, 06:02 AM
  3. derivative.. problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 13th 2010, 06:29 AM
  4. Derivative problem.
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: July 12th 2009, 07:58 AM
  5. Derivative problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 13th 2008, 02:41 AM

Search Tags


/mathhelpforum @mathhelpforum