solve this logarithmic differentiation
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Take the logarithm of the given function: lny=ln(xcosx),⇒lny=cosxlnx. Differentiating the last equation with respect to x, we obtain: (lny)′=(cosxlnx)′,⇒1y⋅y′=(cosx)′lnx+cosx(lnx)′,⇒y′y=(−sinx)⋅lnx+cosx⋅1x,⇒y′y=−sinxlnx+cosxx,⇒y′=y(cosxx−sinxlnx).
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