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Math Help - fractional exponent derivative

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    fractional exponent derivative

    x^1/3 + x. I need to find the second derivative. I came up with -2/ 3x^2/3 for the first..
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    Quote Originally Posted by av8or91 View Post
    x^1/3 + x. I need to find the second derivative. I came up with -2/ 3x^2/3 for the first..
    For differentiation multiply by the exponent before taking one from said exponent

    \frac{d}{dx}(\sqrt [3]{x} +x) = \frac{1}{3\sqrt [3]{x^2}}+1
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  3. #3
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    Quote Originally Posted by av8or91 View Post
    x^1/3 + x. I need to find the second derivative. I came up with -2/ 3x^2/3 for the first..
    Just use the rule: If y = ax^n then \frac{dy}{dx} = anx^{n - 1}.


    So y = x^{\frac{1}{3}} + x

    \frac{dy}{dx} = \frac{1}{3}x^{-\frac{2}{3}} + 1

    \frac{d^2y}{dx^2} = -\frac{2}{9}x^{-\frac{5}{3}}.
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    Thanks, basically trying to find concave up and concave down then the inflection points.
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