Results 1 to 4 of 4

Math Help - Using the definition of the derivative at x=c, compute the following derivatives at a

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    23

    Using the definition of the derivative at x=c, compute the following derivatives at a

    Using the definition of the derivative at x=c, compute the following derivatives at an arbitrary point?

    (a) g(x) = 5x^2

    (b) f(x) = 7x^4

    (c) k(x) = sqrt x

    Please show me the steps cuz I want to learn, not just copying the answer
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    \frac{{k(x + h) - k(x)}}<br />
{h} = \frac{{\sqrt {x + h}  - \sqrt x }}<br />
{h} = \frac{{\sqrt {x + h}  - \sqrt x }}<br />
{h}\frac{{\sqrt {x + h}  + \sqrt x }}<br />
{{\sqrt {x + h}  + \sqrt x }} = \frac{h}<br />
{{h\left[ {\sqrt {x + h}  + \sqrt x } \right]}}

    Now divide out the h's and find the \lim _{h \to 0}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    23
    Quote Originally Posted by Plato View Post
    \frac{{k(x + h) - k(x)}}<br />
{h} = \frac{{\sqrt {x + h} - \sqrt x }}<br />
{h} = \frac{{\sqrt {x + h} - \sqrt x }}<br />
{h}\frac{{\sqrt {x + h} + \sqrt x }}<br />
{{\sqrt {x + h} + \sqrt x }} = \frac{h}<br />
{{h\left[ {\sqrt {x + h} + \sqrt x } \right]}}

    Now divide out the h's and find the \lim _{h \to 0}
    I know this formula, but I don't understand what does x = c mean.

    so, the first one I got lim g(x) = 10x, what do i have to do next
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by jkami View Post
    I know this formula, but I don't understand what does x = c mean.

    so, the first one I got lim g(x) = 10x, what do i have to do next
    No you go g'(x)=the limit=10x, that is the deriviative at the point x is 10x. x is a dummy variable (the logicians have another name for this but I will not bother you with that) it can be replaced with any other symbol denoting a variable, so you also have g'(c)=10c etc.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. compute derivatives
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 13th 2010, 07:30 AM
  2. Compute the 9th derivative
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 17th 2010, 10:03 AM
  3. How to compute this weird derivative?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 11th 2010, 08:18 AM
  4. Replies: 3
    Last Post: May 3rd 2009, 08:44 PM
  5. compute the directional derivatives
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 17th 2008, 03:37 AM

Search Tags


/mathhelpforum @mathhelpforum