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Math Help - Diferentiation

  1. #1
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    Post Diferentiation

    How do you differentiate function like x^(1/4) or x^(3/5) ect?
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  2. #2
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    never mind lololol, d/dx=nx^(n-1)

    for
    f(x)=x^(1/4)
    f'(x)=(1/4)*x^(-3/4)
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  3. #3
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by stripe501 View Post
    How do you differentiate function like x^(1/4) or x^(3/5) ect?
    Given f(x)= x^{\alpha}, where \alpha is an arbitrary real or even complex constant, its derivative by definition is...

    \displaystyle f^{'}(x) = \lim_{\delta \rightarrow 0} \frac{(x+\delta)^{\alpha} - x^{\alpha}}{\delta} (1)

    Now is...

    \displaystyle {(x+\delta)^{\alpha} = x^{\alpha} + \alpha\ \delta\ x^{\alpha-1} + \frac{\alpha\ (\alpha-1)}{2}\ \delta^{2}\ x^{\alpha-2} + ... (2)

    ... so that, combining (1) and (2), we find that is...

    \displaystyle f^{'}(x)= \alpha\ x^{\alpha-1} (3)

    Kind regards

    \chi \sigma
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