Differentiate: y=1+cosx/1-cosx ... ?

The answer for the given question above would be calculated as:

y = (1 + cos (x)) / (1 - cos (x))

Using the quotient rule.

dy/dx = [ (-sin (x)) (1 - cos (x)) - (1 + cos (x)) (sin (x)) ] / [ (1 - cos (x)) ^2 ]

dy/dx = [ - sin (x) + sin (x) cos (x) - sin (x) - sin (x) cos (x) ] / [ 1 - cos (x) ]^2

dy/dx = [ - 2sin (x) ] / [ 1 - cos (x) ]^2

The answer is dy/dx = [ - 2sin (x) ] / [ 1 - cos (x) ]^2