How do I derive this equation in trugonometry?

Question

Ok so the equation goes:

y = 2cosx - cos2x

dy/dx=?

In the answer key in my book they got the derivative:

dy/dx = 2sinxcosx - cosx. How exactly did they get this? From what I am doing I am not getting their answer!

Answer 1

if that 2 in the second term should be interpreted to mean "cosine squared", then dy/dx is as follows

y'=-2sin(x)+2cos(x)sin(x)=
2sin(x)cos(x)-2sin(x)

Answer 2

i cant exactly remember, buut you should dhave a list of formulas somehwere that plus the cos2x into some other thing (like made 2sinxcosx or something i cant remember) and then once you simplifiy you get that answer)

Answer 3

-2sinx+sin2x