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Math Help - Second/Third Derivitive

  1. #1
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    Second/Third Derivitive

    Can anyone help me out in finding the second and third derivitive of radicals like \sqrt{x^2+3}
    Thanks, I can really use some help.
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  2. #2
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    f(x)=\sqrt{x^2+n}, where n is any constant.

    Then using the power rule with the power being 1/2, f'=\frac{1}{2}(x^2+n)^{-\frac{1}{2}} \times 2x=\frac{2x}{2\sqrt{x^2+n})}=\frac{x}{\sqrt{x^2+n}  }

    Now for f'', use the quotient rule. Is this the point where you're having trouble or did this post clear something up?
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  3. #3
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    Im having more trouble finding a way to find the second derivative of that
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  4. #4
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    Well the derivative of u/v is (vu'-vu')/v^2, so just follow the formula and you already know the derivative of v since v is f(x)
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  5. #5
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    I broke the top and bottom of the first derivative into seaparate functions foruse in the product. But I end up with the same equation for the second derivitive as i got in the first. Is this correct?
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