Results 1 to 5 of 5

Math Help - Finding the Derivative of the Given Function

  1. #1
    Junior Member
    Joined
    Jan 2013
    From
    new york
    Posts
    45

    Finding the Derivative of the Given Function

    I am having some difficulty finding the derivative of this equation:

    http://i49.tinypic.com/35jdoxt.png

    Can anyone assist me in solving this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,487
    Thanks
    1391

    Re: Finding the Derivative of the Given Function

    First, I would rewrite the function as \displaystyle \begin{align*} g(x) = \sqrt{10} \, \sqrt{x} \end{align*} and remember that the derivative of a function times a constant is equal to that constant times the derivative. So really, you just need to find the derivative of \displaystyle \begin{align*} \sqrt{x} \end{align*}.

    \displaystyle \begin{align*} f(x) &= \sqrt{x} \\ \\ f(x + h) &= \sqrt{x + h} \\ \\  f'(x) &= \lim_{h \to 0}\frac{f(x+ h) - f(x)}{h} \\ &= \lim_{h \to 0}\frac{\sqrt{x + h} - \sqrt{x}}{h} \\ &= \lim_{h \to 0}\frac{\left( \sqrt{x + h} - \sqrt{x} \right) \left( \sqrt{x + h} + \sqrt{x} \right) }{h \left( \sqrt{x + h} + \sqrt{x} \right) } \\ &= \lim_{h \to 0}\frac{ x + h - x }{h \left( \sqrt{x + h} + \sqrt{x} \right) } \\ &= \lim_{h \to 0}\frac{h}{h \left( \sqrt{x + h} + \sqrt{x} \right) } \\ &= \lim_{h \to 0}\frac{1}{\sqrt{x + h} + \sqrt{x}} \\ &= \frac{1}{\sqrt{x + 0} + \sqrt{x}} \\ &= \frac{1}{\sqrt{x} + \sqrt{x}} \\ &= \frac{1}{2\sqrt{x}} \end{align*}

    Therefore if \displaystyle \begin{align*} g(x) = \sqrt{10} \, \sqrt{x} \end{align*} then \displaystyle \begin{align*} g'(x) = \frac{\sqrt{10}}{2\sqrt{x}} \end{align*}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2013
    From
    new york
    Posts
    45

    Re: Finding the Derivative of the Given Function

    Thanks so much!
    Last edited by michellederz; February 2nd 2013 at 09:05 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,487
    Thanks
    1391

    Re: Finding the Derivative of the Given Function

    Quote Originally Posted by michellederz View Post
    Thank you so much but, apparently the answer can be simplified but I don't see where... Any suggestions on how to simplify the answer you gave?
    What do you consider simpler? What is the expected "simplified" answer? To me, this is the simplest you can get...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2013
    From
    new york
    Posts
    45

    Re: Finding the Derivative of the Given Function

    I figured it out. My math book just had it in a different form for whatever reason..

    It put the answer as:

    5/(square root of 10x)
    Last edited by michellederz; February 2nd 2013 at 09:09 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding derivative of function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 17th 2012, 03:39 PM
  2. Finding the derivative of the function
    Posted in the Calculus Forum
    Replies: 9
    Last Post: May 24th 2011, 06:02 PM
  3. Finding the derivative of this function:
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 2nd 2010, 05:57 PM
  4. Finding derivative of function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 18th 2009, 01:53 PM
  5. Finding the second derivative of a function
    Posted in the Calculus Forum
    Replies: 8
    Last Post: November 13th 2009, 07:17 PM

Search Tags


/mathhelpforum @mathhelpforum