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Thread: differentiation check!!

  1. #1
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    differentiation check!!

    hey can someone check if this is correct. Just a differentiation of a function.

    $\displaystyle

    f (x) = 4x^5 - 13x + 8\sqrt[3]{x} - 9 + (\frac{4}{x}) - (\frac{5}{x^3})

    $

    differentiated to:

    $\displaystyle

    f '(x) = 20x^4 - 13 - 24x^{-4} - (\frac{4}{x^2}) - (\frac{15}{x^4})

    $

    correct?
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  2. #2
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    Quote Originally Posted by jvignacio View Post
    hey can someone check if this is correct. Just a differentiation of a function.

    $\displaystyle

    f (x) = 4x^5 - 13x + 8\sqrt[3]{x} - 9 + (\frac{4}{x}) - (\frac{5}{x^3})

    $

    differentiated to:

    $\displaystyle

    f '(x) = 20x^4 - 13 - 24x^{-4} - (\frac{4}{x^2}) - (\frac{15}{x^4})

    $

    correct?
    Mostly correct except for the derivative of $\displaystyle 8\sqrt[3]{x}$.

    Remember, this is $\displaystyle 8x^{\frac13}$.

    Also, there is a sign error when you differentiated $\displaystyle - \left(\frac{5}{x^3}\right)$.
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  3. #3
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    Not quite. There's a wrong sign at the end, and the differential of the cubic root is not right either. Perhaps you should write it $\displaystyle \sqrt[3]{x}=x^{\frac{1}{3}}$ to ease the differentiation.
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  4. #4
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    $\displaystyle
    f '(x) = 20x^4 - 13 - \frac{8}{3}x^{\frac{-2}{3}} - (\frac{4}{x^2}) + (\frac{15}{x^4})
    $

    better?
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  5. #5
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    Still a problem with the root: the derivative of $\displaystyle \sqrt[3]{x}$ is $\displaystyle +\frac{1}{3}x^{-2/3}$, hence...

    O wait, it just changed. There's still a problem: there is a + in front of the root.
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  6. #6
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    Quote Originally Posted by Laurent View Post
    Still a problem with the root: the derivative of $\displaystyle \sqrt[3]{x}$ is $\displaystyle +\frac{1}{3}x^{-2/3}$, hence...

    O wait, it just changed. There's still a problem: there is a + in front of the root.
    yes i noticed that aswell!!! silly me. thank u for the help
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  7. #7
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    Quote Originally Posted by jvignacio View Post
    hey can someone check if this is correct. Just a differentiation of a function.

    $\displaystyle

    f (x) = 4x^5 - 13x + 8\sqrt[3]{x} - 9 + (\frac{4}{x}) - (\frac{5}{x^3})

    $

    differentiated to:

    $\displaystyle

    f '(x) = 20x^4 - 13 - 24x^{-4} - (\frac{4}{x^2}) - (\frac{15}{x^4})

    $

    correct?
    See here,
    $\displaystyle f (x) = 4x^5 - 13x + 8\sqrt[3]{x} - 9 + (\frac{4}{x}) - (\frac{5}{x^3})$

    $\displaystyle f (x) = 4x^5 - 13x + 8 x^{\frac{1}{3}} - 9 + 4{x}^{-1} - 5x^{-3}$

    Differentiated to:

    $\displaystyle f '(x) = 20x^4 - 13 + \frac{8}{3}x^{\frac{-2}{3}} - (\frac{4}{x^2}) + (\frac{15}{x^4})$

    $\displaystyle f '(x) = 20x^4 - 13 + \frac{8}{\sqrt[3]{x^2}} - (\frac{4}{x^2}) + (\frac{15}{x^4})$
    Last edited by Shyam; Sep 5th 2008 at 11:09 AM.
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