Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Logarithmic differentiation

  1. #1
    Member
    Joined
    Nov 2011
    Posts
    87

    Red face Logarithmic differentiation

    Use logarithmic differentiation to fi nd the derivative of y with respect the independent
    variable x, where

    y = xln x

    thanks to everyone who takes a look
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,506
    Thanks
    1403

    Re: Logarithmic differentiation

    Quote Originally Posted by Nora314 View Post
    Use logarithmic differentiation to find the derivative of y with respect the independent
    variable x, where

    y = xln x

    thanks to everyone who takes a look
    \displaystyle \begin{align*} y &= x^{\ln{x}} \\ \ln{y} &= \ln{\left( x^{\ln{x}} \right)} \\ \ln{y} &= \ln{x}\ln{x} \\ \ln{y} &= \left( \ln{x} \right)^2 \\ \frac{d}{dx} \left( \ln{y} \right) &= \frac{d}{dx} \left[ \left( \ln{x} \right)^2 \right] \\ \frac{d}{dy} \left( \ln{y} \right)\,\frac{dy}{dx} &= \frac{2\ln{x}}{x} \\ \frac{1}{y}\,\frac{dy}{dx} &= \frac{2\ln{x}}{x} \\ \frac{dy}{dx} &= \frac{2y\ln{x}}{x} \\ \frac{dy}{dx} &= \frac{2x^{\ln{x}} \ln{x} }{ x } \end{align*}
    Thanks from Nora314
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2011
    Posts
    87

    Re: Logarithmic differentiation

    Thank you! makes sense now!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. logarithmic differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 9th 2010, 07:44 AM
  2. logarithmic differentiation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 15th 2010, 09:29 PM
  3. logarithmic differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 5th 2009, 03:58 PM
  4. logarithmic differentiation to
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 23rd 2009, 06:52 AM
  5. logarithmic differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 26th 2008, 09:55 AM

Search Tags


/mathhelpforum @mathhelpforum