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Math Help - Differentiating with roots and powers.

  1. #1
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    Differentiating with roots and powers.

    Hi all,

    I have started reading Calculus Made Easy by Silvanus P.Thompson and am having a little difficulty early in.

    The problem is

    y=\sqrt[q]{x^{3}}

    and I have \frac{dy}{dx}=\frac{3}{q}x^{\frac{3}{q}-1}

    but the solution is \frac{3}{q}x^{\frac{3-q}{q}}

    My workings are

    y=\sqrt[q]{x^{3}}=x^{\frac{3}{q}}, \frac{dy}{dx}=\frac{3}{q}x^{\frac{3}{q}-1}

    I thought that during the differentiation the index is reduced by 1?

    Any help would be great,

    thanks.
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  2. #2
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    e^(i*pi)'s Avatar
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    Re: Differentiating with roots and powers.

    Quote Originally Posted by Srengam View Post
    Hi all,

    I have started reading Calculus Made Easy by Silvanus P.Thompson and am having a little difficulty early in.

    The problem is

    y=\sqrt[q]{x^{3}}

    and I have \frac{dy}{dx}=\frac{3}{q}x^{\frac{3}{q}-1}

    but the solution is \frac{3}{q}x^{\frac{3-q}{q}}

    My workings are

    y=\sqrt[q]{x^{3}}=x^{\frac{3}{q}}, \frac{dy}{dx}=\frac{3}{q}x^{\frac{3}{q}-1}

    I thought that during the differentiation the index is reduced by 1?

    Any help would be great,

    thanks.
    The two answers are the same (and correct). The book have wrote 1 as q/q.


    \dfrac{3}{q} -1 = \dfrac{3}{q} - \dfrac{q}{q} = \dfrac{3-q}{q}
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  3. #3
    Junior Member
    Joined
    Jun 2011
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    37

    Re: Differentiating with roots and powers.

    Many thanks, that helps a lot.
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