Results 1 to 2 of 2

Math Help - Finding the Derivative...

  1. #1
    Member
    Joined
    Dec 2009
    Posts
    96

    Finding the Derivative...

    We are just being introduced the the derivative concept and I was wondering if I understand this correctly.

    We got the formula f(x) lim h->0 (f(x+h) - f(x)) / h

    One example says: Find derivative for the function f(x)=x/(x-1)

    Does this like correct:

    1. (x/x-1+h) - (x/(x-1) / h
    The x/x-1 - x/x-1 cancel out
    Leaving you with H/H
    so the derivative is 1??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2009
    Posts
    69
    If f(x) = \frac{x}{x-1}, then f(x+h) = \frac{x+h}{x+h-1} (you have to replace every x with x+h). Then...

    f(x+h) - f(x) = \frac{x+h}{x+h-1} - \frac{x}{x-1} = \frac{(x+h)(x-1)-x(x+h-1)}{(x+h-1)(x-1)}

    =\frac{x(x-1)+hx-h-x(x-1)-hx}{(x+h-1)(x-1)}=\frac{-h}{(x+h-1)(x-1)}

    Dividing by h and taking the limit as h goes to 0, you get \frac{-1}{(x-1)^2}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the derivative
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 13th 2010, 03:27 PM
  2. finding the derivative of sin^2(x)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 3rd 2010, 01:34 AM
  3. finding derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 13th 2009, 10:21 PM
  4. finding derivative dy / dx
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 21st 2009, 01:01 PM
  5. Finding this derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 3rd 2008, 12:34 PM

Search Tags


/mathhelpforum @mathhelpforum