Results 1 to 5 of 5

Math Help - logarithmetic differentiation

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    34

    logarithmetic differentiation

    I need to find dx/dy using logarithmetic differentiation. Thanks for any help!!

    1. y = sqrt((x-1) (x-2) (x-3))

    2. y= sqrt((x^2-2)/(x^2+2))
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    Shouldn't it be \frac{dy}{dx}\,?

    y=\sqrt{(x-1)(x-2)(x-3)}=\exp\left(\frac12\ln\Big[(x-1)(x-2)(x-3)\Big]\right).

    Now take the derivative.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by SMAlvarez View Post
    I need to find dx/dy using logarithmetic differentiation. Thanks for any help!!

    1. y = sqrt((x-1) (x-2) (x-3))
    Krizalid is correct. but in my experience, logarithmic differentiation is done this way:

    y = \sqrt{(x - 1)(x - 2)(x - 3)} = [(x - 1)(x - 2)(x - 3)]^{\frac 12}

    take the log of both sides

    \Rightarrow \ln y = \ln [(x - 1)(x - 2)(x - 3)]^{\frac 12}

    \Rightarrow \ln y = \frac 12 \left[ \ln (x - 1) + \ln (x - 2) + \ln (x - 3) \right]

    Now differentiate implicitly.


    of course Krizalid's method is equivalent, the difference is, you do not have to differentiate implicitly with his method, explicit differentiation works
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2007
    Posts
    34
    so is the final answer :

    1/2[(1/x-1)+(1/x-2)+(1/x-3)]

    ?

    How would I start the second one?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by SMAlvarez View Post
    so is the final answer :

    1/2[(1/x-1)+(1/x-2)+(1/x-3)]

    ?

    How would I start the second one?
    no. recall that we have ln y on the left hand side. you must differentiate implicitly and simplify accordingly

    the second one is done in exactly the same way, start by logging both sides and splitting up the logs
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 26th 2010, 06:24 PM
  2. Differentiation and partial differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 30th 2010, 11:16 PM
  3. Logarithmetic Differentiation?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 7th 2009, 07:26 PM
  4. Differentiation and Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 6th 2009, 05:07 AM
  5. Two logarithmetic problems, solve for x
    Posted in the Algebra Forum
    Replies: 5
    Last Post: December 18th 2008, 10:39 AM

Search Tags


/mathhelpforum @mathhelpforum