What is the derivative of #(cot^(2)x)#?

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Answer 1 · 2016-01-09T04:54:12

#frac{d}{dx}(cot^2x) = frac{-2cosx}{sin^3x}#

#frac{d}{dx}(cot^2x) = 2cot(x)*frac{d}{dx}(cotx)#

#= 2cotx*frac{d}{dx}(cosx/sinx)#

#= 2cotx*frac{sinxfrac{d]{dx}(cosx)-cosxfrac{d}{dx}(sinx)}{sin^2x}#

#= 2cotx*frac{sinx(-sinx)-cosx(cosx)}{sin^2x}#

#= 2cotx*frac{-(sin^2x+cos^2x)}{sin^2x}#

#= 2frac{cosx}{sinx}*frac{-1}{sin^2x}#

#= frac{-2cosx}{sin^3x}#