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Math Help - Help with Derivatives

  1. #1
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    Help with Derivatives

    I need some help solving these derivative problems:

    1. F(x)= 3rd root of(x)-[1/3rd root of(x)]
    For this one I got: 1/3 x - 3rd root of(9)

    2. (s^2+s+1)^4 * (s-2)^7
    I tried doing this one but it got out of hand and messy.

    Any help would be great.
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  2. #2
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    Before I work this through, tell me if this is what the equation is:
    <br />
x^3 - \sqrt[3]{x}<br />
    and
    <br />
(s^2 + s + 1)^4 * (s-2)^7<br />
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  3. #3
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    yep that's them.

    For future reference how do you do that (make math symbols visible and all)

    -thankx
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  4. #4
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    Just use this tutorial: http://www.mathhelpforum.com/math-he...-tutorial.html

    Now to help you with your first problem:

    f(x) = x^3 - {x}^\frac {1}{3}

    From here, you will want to use the power rule so:

    f'(x) = 3x^2 - \frac {x}{3}^ {\frac {1}{3} - 1} =
    3x^2 - \frac {x}{3}^ {\frac {-2}{3}}

    Now for the second you will need to use the chain rule and the product rule.

    <br />
f(x) = (s^2 + s + 1)^4 * (s-2)^7<br />

    <br />
f'(x) = (s^2 + s + 1)^4 * 7(s-2)^6 + (s-2)^7 * 8s(s^2 + s + 1)^3<br />
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  5. #5
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    Quote Originally Posted by JoshHJ View Post
    Just use this tutorial: http://www.mathhelpforum.com/math-he...-tutorial.html

    Now to help you with your first problem:

    f(x) = x^3 - {x}^\frac {1}{3}

    From here, you will want to use the power rule so:

    f'(x) = 3x^2 - \frac {x}{3}^ {\frac {1}{3} - 1} = 3x^2 - \frac {x}{3}^ {\frac {-2}{3}}

    Now for the second you will need to use the chain rule and the product rule.

    f(x) = (s^2 + s + 1)^4 * (s-2)^7

    f'(x) = (s^2 + s + 1)^4 * 7(s-2)^6 + (s-2)^7 * 8s(s^2 + s + 1)^3
    I think you might have meant f({\color{red}s}) = (s^2 + s + 1)^4 * (s-2)^7

    and

    f'({\color{red}s}) = (s^2 + s + 1)^4 * 7(s-2)^6 + (s-2)^7 * {\color{red}4(2s+1)} (s^2 + s + 1)^3.
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  6. #6
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    Quote Originally Posted by roksteady View Post
    yep that's them.

    [snip]
    Clearly not, since you re-posted the cube root one ....

    Quote Originally Posted by roksteady
    5. \sqrt[3]{x}-1/\sqrt[3]{x}
    I got: 1/3x^(-2/3) + 1/3x^(-4/3)
    Your answer is correct.

    Note: The derivative of the first term is done as has already been shown in this thread.

    However, I'm glad to see you learned some latex
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