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Math Help - Differentiation from first principles

  1. #1
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    Differentiation from first principles

    2x^2 - x - 8

    i get to

    4xdeltax + 2(deltax)^2 - deltax

    the 2(deltax)^2 part is confusing me I get the answer 4x but it's supposed to be 4x - 1

    thanks for any help
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  2. #2
    Eater of Worlds
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    \lim_{h\to 0}\frac{2(x+h)^{2}-(x+h)-8-(2x^{2}-x-8)}{h}

    Expanding the top and we get:

    \lim_{h\to 0}\frac{2x^{2}+4xh+2h^{2}-x-h-8-2x^{2}+x+8}{h}

    Note that many of the terms in the top cancel one another and we are left with:

    \lim_{h\to 0}\frac{4xh+2h^{2}-h}{h}

    \lim_{h\to 0}4x+2h-1

    See what's left?. The derivative of 2x^{2}-x-8
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  3. #3
    MHF Contributor Calculus26's Avatar
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    When you divide 4xdeltax + 2(deltax)^2 - deltax by deltax

    you get 4x +2deltax - 1

    letting delta x -> 0 you get 4x -1
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  4. #4
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    It's the -1 that I dont't get, am I to assume -deltax divided by deltax is -1
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  5. #5
    MHF Contributor Calculus26's Avatar
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    -2/2 = -1

    -f/f = -1

    -anything/anything = -1

    -dx/ddx = -1
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