Results 1 to 2 of 2

Math Help - Def. of Derivative.

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    1

    Def. of Derivative.

    How do you find the definition of f(x)=x (sq. root(x+1))
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by EEElliott View Post
    How do you find the definition of f(x)=x (sq. root(x+1))
    How far did you get?

    f'(x)=\lim_{h\to 0}\frac{(x+h)\sqrt{x+h+1}-x\sqrt{x+1}}{h}

    I'm sure you got stuck here. The thing we need to do now is multiply by the conjugate of the numerator:

    f'(x)=\lim_{h\to 0}\frac{(x+h)\sqrt{x+h+1}-x\sqrt{x+1}}{h}\cdot\frac{(x+h)\sqrt{x+h+1}+x\sqrt  {x+1}}{(x+h)\sqrt{x+h+1}+x\sqrt{x+1}}

    This simplifies to \lim_{h\to 0}\frac{(x+h)^2(x+h+1)-x^2(x+1)}{h\left[(x+h)\sqrt{x+h+1}+x\sqrt{x+1}\right]}

    Expand out the numerator, and try to cancel out as many terms as you can. Then a common factor of h should appear in all the numerator terms. Pull it out, and it should then cancel out with the h term in the denominator. Then evaluate the limit.

    Can you try to take it from here?

    --Chris
    Last edited by Chris L T521; October 9th 2008 at 07:29 PM.
    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, 02:37 AM
  2. Replies: 0
    Last Post: January 24th 2011, 11:40 AM
  3. [SOLVED] Definition of Derivative/Alt. form of the derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 23rd 2010, 06:33 AM
  4. Derivative Increasing ==> Derivative Continuous
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 23rd 2010, 10:58 AM
  5. Replies: 2
    Last Post: November 6th 2009, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum