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Math Help - The definition of a derivative

  1. #1
    Member purplec16's Avatar
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    The definition of a derivative

    f(x)=\frac{3}{2x+1}

    I got

    the limit = 3(\frac{-2}{ (2x+1)^2})
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  2. #2
    Super Member TheChaz's Avatar
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    When you use the definition, the limit will involve (depending on the form you use), the letter h, a, x_0, or delta x.

    You should have
    \lim_{x \to h}\frac{f(x + h) - f(x)}{h}

    \lim_{x \to h}\frac{\frac{3}{2(x + h) + 1} - \frac{3}{2x + 1}}{h}

    for starters, at least.
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  3. #3
    Member purplec16's Avatar
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    I have that, I'm trying to check my answer and that is where I got stuck I would type it all out but i'm extremely tired
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  4. #4
    Super Member TheChaz's Avatar
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    Quote Originally Posted by purplec16 View Post
    I have that, I'm trying to check my answer and that is where I got stuck I would type it all out but i'm extremely tired
    For f(x) = 3/(2x + 1)
    f'(x) = -6/(2x + 1)^2 , which is what you have (after simplifying).

    You can check using wolfram... y = 3/(2x + 1) - Wolfram|Alpha
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