Results 1 to 3 of 3

Math Help - Differentiability

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    91

    Differentiability

    Using the fact that  x \rightarrow logx is differentiable on  (0,\infty) with derivative  x \rightarrow \frac {1} {x} verify that  arctanh x=\frac {1} {2} log ( \frac {1+x} {1-x}) is differentiable and compute its derivative. Now I have no problem finding the derivative, however I'm not sure how to show it is differentiable. It shouldn't be too hard but I'm not too acquainted with the method. Thanks!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    tah
    tah is offline
    Junior Member
    Joined
    Feb 2009
    Posts
    51
    Quote Originally Posted by nmatthies1 View Post
    Using the fact that  x \rightarrow logx is differentiable on  (0,\infty) with derivative  x \rightarrow \frac {1} {x} verify that  arctanh x=\frac {1} {2} log ( \frac {1+x} {1-x}) is differentiable and compute its derivative. Now I have no problem finding the derivative, however I'm not sure how to show it is differentiable. It shouldn't be too hard but I'm not too acquainted with the method. Thanks!!
    Hi, I think you must specify that it's differentiable somewhere. Indeed it's only well defined for  x\in]-1,1[ , so you can use the result on the composition of differentiable functions in that interval.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2008
    Posts
    91
    makes sense. thanks!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. differentiability
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 16th 2012, 06:31 AM
  2. Differentiability
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 13th 2010, 11:45 AM
  3. Differentiability
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 21st 2010, 07:16 PM
  4. Differentiability
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 20th 2009, 11:14 AM
  5. Differentiability
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 30th 2008, 01:08 PM

Search Tags


/mathhelpforum @mathhelpforum