What is the d/dx of cosx / sin^2x?

Answer 1

y = cosx / sin²x

Using the Quotient Rule, dy/dx = [sin²x(-sinx) - cosx(2sinxcosx)] / sin⁴x =

[-sin³x - 2sinxcos²x] / sin⁴x = [-sin³x - 2sinx(1 - sin²x)] / sin⁴x

= [sin³x - 2sinx] / sin⁴x = sinx(sin²x - 2) / sin⁴x = (sin²x - 2) / sin³x