Results 1 to 4 of 4

Math Help - Natural log problem

  1. #1
    Member ~berserk's Avatar
    Joined
    Apr 2008
    Posts
    82

    Natural log problem

    Differentiate: h(t)= ln((t^2+1)/(t+1))

    I'm having some trouble with this one. Not sure if I am doing too much work for it.

    Also this one: y= x^x^2

    Do I have to use logarithmic differentiaton for the second?
    Last edited by ~berserk; November 13th 2012 at 09:09 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Natural log problem

    For the second one, another option besides logarithmic differentiation is exponential differentiation:

    y=x^{x^2}=e^{\ln\left(x^{x^2} \right)}=e^{x^2\ln(x)}

    Now use the exponential, chain and product rules to find the derivative.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member ~berserk's Avatar
    Joined
    Apr 2008
    Posts
    82

    Re: Natural log problem

    would you be able to show me how to differentiate it logarithmically?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Natural log problem

    We are given to differentiate:

    y=x^{x^2}

    Take the natural log. of both sides:

    \ln(y)=\ln\left(x^{x^2} \right)=x^2\ln(x)

    Now, implicitly differentiate both sides with respect to x. I don't want to just work out the whole thing, but I will help guide you if you get stuck.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Natural Log problem, please can you help?
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 30th 2011, 12:28 PM
  2. Natural log problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 18th 2011, 02:56 AM
  3. Natural Log Problem
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 19th 2010, 05:48 PM
  4. Natural log problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 6th 2009, 07:20 PM
  5. Natural log problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 1st 2009, 04:04 PM

Search Tags


/mathhelpforum @mathhelpforum