求函数y=cot(lnx)的导数

2个回答

  • 利用复合函数的求导法则:y= f(u),u= u(x),则 f ' (x) = f '(u) * u'(x)

    y = cot ( lnx),设:y = cot u,u= lnx

    y ' = (cotu)' = ( sinu/ cosu) ' = [ (sinu)' *cosu - sinu * ( cosu)' ]/ (cosu)^2

    = (cos^2u + sin^2u) /( cos^2u) = 1/ cos^2u

    u ' = (lnx)' =1/x

    所以:y ' = 1/ ([cos^2( lnx)] * x)