Question

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

Answer 1

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