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Math Help - Derivative

  1. #1
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    Derivative

    By using the power rule, how can i find the derivative of:

    (x-1)^2 *x / x^1/3


    I just dont know how to do the numerator..

    should i take the 2 infront and then simplify or sould i resolve the power, into (x-1)(x-1) ???
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  2. #2
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    Quote Originally Posted by HHHH View Post
    By using the power rule, how can i find the derivative of:

    (x-1)^2 *x / x^1/3


    I just dont know how to do the numerator..

    should i take the 2 infront and then simplify or sould i resolve the power, into (x-1)(x-1) ???
    note that \frac{x}{x^{\frac{1}{3}}} = x^{\frac{2}{3}}

    \frac{d}{dx} \left[(x-1)^2 \cdot x^{\frac{2}{3}} \right]

    product rule ...

    (x-1)^2 \cdot \frac{2}{3}x^{-\frac{1}{3}} + x^{\frac{2}{3}} \cdot 2(x-1)
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  3. #3
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    Quote Originally Posted by skeeter View Post
    note that \frac{x}{x^{\frac{1}{3}}} = x^{\frac{2}{3}}

    \frac{d}{dx} \left[(x-1)^2 \cdot x^{\frac{2}{3}} \right]

    product rule ...

    (x-1)^2 \cdot \frac{2}{3}x^{-\frac{1}{3}} + x^{\frac{2}{3}} \cdot 2(x-1)

    thanx, but how or why did you do the last part, +x^2/3 * 2(x-1) ?
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  4. #4
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    Quote Originally Posted by HHHH View Post
    thanx, but how or why did you do the last part, +x^2/3 * 2(x-1) ?
    He held x^{\frac{2}{3}} constant and took the derivative of (x-1)^2, which is 2(x-1). This is how the product rule works. d(ab)=a'b+b'a
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