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Thread: Finding derivative example

  1. #1
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    Question Finding derivative example

    Hi,

    I hope someone can help. I'm trying to find the derivative at x = 4 for the following equation:
    Finding derivative example-screen-shot-2017-07-26-12.31.24-pm.png

    For some reason, I get the wrong solution when I don't factor out the expression before finding the derivative:
    Finding derivative example-20447023_1483465735042849_1190873935_o.jpg


    The actual solution for f^1(4) is apparently 12:
    Finding derivative example-screen-shot-2017-07-26-12.37.12-pm.png

    Help would be very much appreciated!
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  2. #2
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    Re: Finding derivative example



    product rule ...

    $f'(x) = (1+2x^{0.5})(-1 + 1.5x^{0.5}) + (-x+x^{1.5})(x^{-0.5})$

    $f'(4) = (1+4)(-1+3) + (-4+8)\left(\dfrac{1}{2}\right) = 10 + 2 = 12$
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  3. #3
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    Re: Finding derivative example

    In other words, (fg)' is not equal to f'g'. It is, as skeeter said, f'g+ fg'.
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  4. #4
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    Re: Finding derivative example

    okay good to know. I wasn't aware of the product rule until now... so thanks!
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