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Math Help - What's the derivative of (1/3x^2)?

  1. #1
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    What's the derivative of (1/3x^2)?

    What's the derivative of (1/3x^2)? I dont really understand how to use the power rule with this one. I know its Y'=Nx^N-1 but how do I put this fraction into something like that? Is it like 3x^-3? then taking the derivative of that becomes -9^-4???? The entire quiestion is (1/3x^-2) - (5/2x) I dont understand how to find the derivative of the other side either really. Help GREATLY appreciated.
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  2. #2
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    Quote Originally Posted by jmoh View Post
    What's the derivative of (1/3x^2)? I dont really understand how to use the power rule with this one. I know its Y'=Nx^N-1 but how do I put this fraction into something like that? Is it like 3x^-3? then taking the derivative of that becomes -9^-4???? The entire quiestion is (1/3x^-2) - (5/2x) I dont understand how to find the derivative of the other side either really. Help GREATLY appreciated.
    <br />
\frac{d}{dx} \left[\frac{1}{3x^2}\right]= \frac{1}{3}~\frac{d}{dx}\left[ \frac{1}{x^2}\right]= \frac{1}{3}~\frac{d}{dx} \left[ x^{-2} \right]<br />

    Then apply the power rule to x^{-2} with N=-2

    RonL
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    Quote Originally Posted by jmoh View Post
    What's the derivative of (1/3x^2)? I dont really understand how to use the power rule with this one. I know its Y'=Nx^N-1 but how do I put this fraction into something like that? Is it like 3x^-3? then taking the derivative of that becomes -9^-4???? The entire quiestion is (1/3x^-2) - (5/2x) I dont understand how to find the derivative of the other side either really. Help GREATLY appreciated.
    y=\frac{1}{3x^2} = \frac{1}{3}x^{-2}

    \implies y' = \frac{1}{3} \cdot (-2) \cdot x^{-2-1}
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    Thanks guys!
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