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Math Help - Help please: Compute the derivative function

  1. #1
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    Help please: Compute the derivative function

    Here's the problem:

    f(x) = \frac{2}<br />
{{2x - 1}}

    Here's what I did so far...I have no idea if I'm even on the right track..


    f'(x) = \mathop {\lim }\limits_{h \to 0} \frac{{\frac{2}<br />
{{2(x + h) - 1}} - \frac{2}<br />
{{2x - 1}}}}<br />
{h}



     = \mathop {\lim }\limits_{h -  > 0} \frac{{\frac{{4x - 2 - 4x - 4h + 2}}<br />
{{2x - 1(2x + 2h - 1)}}}}<br />
{h} = \mathop {\lim }\limits_{h -  > 0} \frac{{\frac{{ - 4h}}<br />
{{2x - 1(2x + 2h - 1)}}}}<br />
{h}
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    These things are mostly about the algebra. As you can well see.

    \lim_{h\rightarrow{h}}\frac{\frac{2}{2(x+h)-1}-\frac{2}{2x-1}}{h}

    =\lim_{h\rightarrow{h}}\left[\frac{2}{h(2x+2h-1)}-\frac{2}{h(2x-1)}\right]

    Now, factor:

    =\lim_{h\rightarrow{h}}\frac{-4}{(2x-1)(2x+2h-1)}

    Now, see it?.
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  3. #3
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    Would I just set  h = 0 which leaves me with

    <br />
-4 / (2x-1)^2
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  4. #4
    Flow Master
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    Quote Originally Posted by toop View Post
    Would I just set  h = 0 which leaves me with

    <br />
-4 / (2x-1)^2
    Yes.
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