Results 1 to 4 of 4

Math Help - derivative of a^x

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    249

    derivative of a^x

    i am trying to find the derivative of a^x using the limit definition of the derivative.

    in order to find the derivative of a^x i need to show:
    lim (a^h - 1) / h = ln(a)
    h~>0

    i can't see any obvious way to manipulate the expression so that i get ln a in the end. please help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by oblixps View Post
    i am trying to find the derivative of a^x using the limit definition of the derivative.

    in order to find the derivative of a^x i need to show:
    lim (a^h - 1) / h = ln(a)
    h~>0

    i can't see any obvious way to manipulate the expression so that i get ln a in the end. please help.
    You will struggle using this approach I think. Read section 3 and 4 here: http://www.mash.dept.shef.ac.uk/Reso...b-logs-exp.pdf
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2008
    Posts
    249
    Quote Originally Posted by mr fantastic View Post
    You will struggle using this approach I think. Read section 3 and 4 here: http://www.mash.dept.shef.ac.uk/Reso...b-logs-exp.pdf
    thanks! is there any way to do that limit algebraically though?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by oblixps View Post
    thanks! is there any way to do that limit algebraically though?
    Not without knowing what the derivative of a^x is ....!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 22nd 2011, 03:37 AM
  2. Replies: 0
    Last Post: January 24th 2011, 12:40 PM
  3. [SOLVED] Definition of Derivative/Alt. form of the derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 23rd 2010, 07:33 AM
  4. Derivative Increasing ==> Derivative Continuous
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 23rd 2010, 11:58 AM
  5. Replies: 2
    Last Post: November 6th 2009, 03:51 PM

Search Tags


/mathhelpforum @mathhelpforum