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Math Help - Natural Log Differentiation

  1. #1
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    Natural Log Differentiation

    I have a problem here that I am not sure is correct.

    We have been asked to find the derivative of the following funciton:

    ln{(x(x^2+5))/sqrt(x^3-5)}
    I realize this looks really sloppy.

    The answer that I have arrived at is

    {((2x^2 + 5) - sqrt(3x^2))/2}

    Any help would be greatly appreciated
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  2. #2
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by CrEpE View Post
    I have a problem here that I am not sure is correct.

    We have been asked to find the derivative of the following funciton:

    ln{(x(x^2+5))/sqrt(x^3-5)}
    I realize this looks really sloppy.

    The answer that I have arrived at is

    {((2x^2 + 5) - sqrt(3x^2))/2}

    Any help would be greatly appreciated
    \frac{d}{dx}ln({\frac{x(x^2+5)}{\sqrt{x^3-5}}}) = \frac{\sqrt{x^3-5}}{x(x^2+5)}\times \frac{d}{dx}[\frac{x(x^2+5)}{\sqrt{x^3-5}}] = \frac{\sqrt{x^3-5}}{x(x^2+5)}\times \frac{\sqrt{x^3-5}\frac{d}{dx}[x(x^2+5)] - x(x^2+5)\frac{d}{dx}[\sqrt{x^3-5}]}{(\sqrt{x^3-5})^2}

    Can you take it from here?
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  3. #3
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    Yes I believe so. Maybe I just oversimplified it
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