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Math Help - Radical derivative problem, dude

  1. #1
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    Radical derivative problem, dude

    I need to find the derivative of f(x) = 5e^x * x^{\frac{1}{6}}

    So far I've gotten 5e^x * \frac{1}{6} * x^{\frac{-5}{6}}
    However, I'm uncertain where to go next.
    I thought x^{\frac{-5}{6}} = \frac{1}{x^{\frac{5}{6}}}
    Ergo I would end up with \frac{5e^x}{6x^{5/6}}

    That's obviously wrong, though...
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  2. #2
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    Re: Radical derivative problem, dude

    Quote Originally Posted by Nervous View Post
    I need to find the derivative of f(x) = 5e^x * x^{\frac{1}{6}}

    So far I've gotten 5e^x * \frac{1}{6} * x^{\frac{-5}{6}}
    However, I'm uncertain where to go next.
    I thought x^{\frac{-5}{6}} = \frac{1}{x^{\frac{5}{6}}}
    Ergo I would end up with \frac{5e^x}{6x^{5/6}}

    That's obviously wrong, though...
    You have a product, so you need to use the Product Rule.

    \displaystyle \begin{align*} \frac{d}{dx}\left[f(x)\,g(x)\right] &= f(x)\,\frac{d\,g(x)}{dx} + g(x)\,\frac{d\,f(x)}{dx} \end{align*}
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