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calculus

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y = (ln x)^(cos4x)
Use logarithmic differentiation to find the derivative of the function.

  • calculus -

    lny = ln[(lnx)^(cos(4x))]
    = cos(4x) * ln(ln(x))
    y'/y = cos(4x)*1/ln(x) * 1/x + ln(ln(x))(-4sin(4x)

    y' = (ln x)^(cos4x) [cos(4x)*1/ln(x) * 1/x + ln(ln(x))(-4sin(4x) ]

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