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Math Help - Finding Derivatives of Radicals

  1. #1
    Junior Member alane1994's Avatar
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    Finding Derivatives of Radicals

    How does one find the derivative of a radical? Ex. \sqrt{x+6}
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    MHF Contributor MarkFL's Avatar
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    Re: Finding Derivatives of Radicals

    Rewrite the function using a rational exponent, then use the power rule:

    f(x)=\sqrt{x+6}=(x+6)^{\frac{1}{2}} and so:

    f'(x)=\frac{1}{2}(x+6)^{-\frac{1}{2}}=\frac{1}{2\sqrt{x+6}}
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  3. #3
    Junior Member alane1994's Avatar
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    Re: Finding Derivatives of Radicals

    So, for the second derivative you would use the quotient rule right? And how would that work? You would have to find the derivative of 2\sqrt{x+6} which I believe is -\sqrt{x+6}... am I on the right track?
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    Re: Finding Derivatives of Radicals

    Quote Originally Posted by alane1994 View Post
    How does one find the derivative of a radical? Ex. \sqrt{x+6}
    Here is a formula that is most useful. If f(x) is a differentiable function and y=\sqrt{f(x)} then y^{\prime}=\frac{f^{\prime}(x)}{2\sqrt{f(x)}}.

    Learning that form can be a great time saver.
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  5. #5
    Junior Member alane1994's Avatar
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    Re: Finding Derivatives of Radicals

    Awesome, that is a cool way to think of it!
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