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

Question

2558 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-09T04:54:12

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

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

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

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

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

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

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

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

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