Question

If Y=sin2x/cosx than dy/dx is

Answer 1

using the quotient rule,

dy/dx = [2cos2x * cosx - sin2x(-sinx)]/cos^2x

= [2(1-2sin^2x)(cosx) + (2sinx cosx)(sinx)]/cos^2x

= [2cosx - 4sin^2x cosx + 2sin^2x cosx]/cos^2x

= (2cosx - 2sin^2x cosx)/cos^2x
= 2cosx(1-sin^2x)/cos^2x
= 2cosx cos^2x/cos^2x
= 2cosx

Of course, you could avoid all that mess by noting that

sin2x/cosx = (2sinx cosx)/cosx = 2sinx