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chetibaby
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Tyro
Asked: 2021-01-10T22:53:56+00:00 In:

Differentiate with respect to x: \sqrt[3]{6x+1}

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Differentiate with respect to x: \sqrt[3]{6x+1}

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  2. Sengemegz
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    This answer was edited.

    y=\sqrt[3]{6x+1}
    Let u=(6x+1) then y=u^{\frac{1}{3}}
    and \dfrac{du}{dx}=6 then \dfrac{dy}{du}=\dfrac{1}{3}u^{-\frac{2}{3}}
    \dfrac{dy}{dx}=\dfrac{du}{dx}\times \dfrac{dy}{du}
    \Rightarrow \dfrac{dy}{dx}=6\times \dfrac{1}{3}u^{-\frac{2}{3}}
    \Rightarrow \dfrac{dy}{dx}=\dfrac{6}{3}u^{-\frac{2}{3}}
    \Rightarrow \dfrac{dy}{dx}=\dfrac{6}{3u^{\frac{2}{3}}}
    \therefore \dfrac{dy}{dx}=\dfrac{2}{(\sqrt[3]{6x+1})^{2}}

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