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Math Help - Derivative problem

  1. #1
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    Derivative problem

    This is a problem for finding the f'(x) of  x^3 from a definition for a derivative which is derived from the definition for m_{tan}:

    f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}

    So, after plugging in the function

    f'(x)=\lim_{h\to0}\frac{(x+h)^3-x^3}{h} and doing some mad Algebra, I get to this point

    <br />
 =\lim_{h\to0}\frac{x^3+h^3+3h^2x+3x^2h}{h}<br />

    and don't know where to go. Can anyone help?

    I think that maybe I missed or am blocking this bit of Algebra. A link to a relevant online Algebra reference text would also be appreciated.
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  2. #2
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    Quote Originally Posted by mathbit View Post
    This is a problem for finding the f'(x) of  x^3 from a definition for a derivative which is derived from the definition for m_{tan}:

    f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}

    So, after plugging in the function

    f'(x)=\lim_{h\to0}\frac{(x+h)^3-x^3}{h} and doing some mad Algebra, I get to this point

    <br />
=\lim_{h\to0}\frac{x^3+h^3+3h^2x+3x^2h}{h}<br />

    and don't know where to go. Can anyone help?

    I think that maybe I missed or am blocking this bit of Algebra. A link to a relevant online Algebra reference text would also be appreciated.
    You're missing a term. It should be (in red)

    <br />
=\lim_{h\to0}\frac{x^3+h^3+3h^2x+3x^2h - \color{red}{x^3}}{h}<br />
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  3. #3
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    Doh!
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