Results 1 to 2 of 2

Math Help - Natural log differentiation

  1. #1
    Member nautica17's Avatar
    Joined
    Aug 2009
    Posts
    121

    Natural log differentiation

    Could someone kindly show me the steps involved in solving the following.

    y = ln(x/1+x^2)


    The answer should come out to dy/dx = (1-x^2)/x(1+x^2), but I don't know exactly how this was achieved.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by nautica17 View Post
    Could someone kindly show me the steps involved in solving the following.

    y = ln(x/1+x^2)


    The answer should come out to dy/dx = (1-x^2)/x(1+x^2), but I don't know exactly how this was achieved.
    First remember the property of logs that

    \ln\left( \frac{A}{B} \right)=\ln(A)-\ln(B)

    so we get

    y=\ln(x)-\ln(1+x^2)

    Now using the chain rule we get

    y'=\frac{1}{x}-\frac{2x}{1+x^2}

    Now simplifying we get

    y'=\frac{1+x^2}{x(1+x^2)}-\frac{2x^2}{x(1+x^2)}=\frac{1-x^2}{x(1+x^2)}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 28th 2011, 09:16 AM
  2. natural differentiation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 1st 2011, 07:12 PM
  3. Natural Log Differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 6th 2010, 08:17 PM
  4. Implicit natural log differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 17th 2010, 08:28 PM
  5. Implicit Differentiation w/ Natural Log
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 22nd 2009, 08:22 AM

Search Tags


/mathhelpforum @mathhelpforum