Calculus

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y=x^logbase5(x)

  • Calculus -

    lny = log_5(x) lnx
    = lnx/ln5 lnx
    = 1/ln5 ln^2(x)

    1/y y' = 1/ln5 * 2lnx * 1/x
    y' = 2y lnx / x ln5
    = 2lnx/ln5 x^(log_5(x)-1)
    = 2log_5(x) x^(log_5(x)-1)

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