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logarithmic differentiation

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How do you find the logarithmic differentiation of y = x^-cos x ?

  • logarithmic differentiation - ,

    first take ln of both sides

    ln y = ln(x^-cosx)
    ln y = -cosx lnx

    now differentiate with respect to x
    (dy/dx)/y = -cosx (1/x) + lnx (sinx)

    dy/dx = y ( -(1/x)cosx + lnx(sinx))
    = x^-cosx ( -(1/x)cosx + lnx(sinx))

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