Answer:
Explanation:
We can find dy/dx by differentiating y with respect to x using the quotient rule.
First, we need to rewrite y using the trigonometric identity for the tangent of the difference of two angles:
y = (cos x - sin x)/(cos x + sin x) = [(cos x - sin x)/(cos x + sin x)] * [(cos x - sin x)/(cos x - sin x)]
y = (cos^2 x - 2cos x sin x + sin^2 x)/(cos^2 x - 2sin x cos x + sin^2 x)
y = (cos 2x - sin 2x)/(cos 2x + sin 2x)
Now we can apply the quotient rule:
dy/dx = [(-sin 2x - cos 2x)(cos 2x + sin 2x) - (cos 2x - sin 2x)(-sin 2x + cos 2x)]/(cos 2x + sin 2x)^2
dy/dx = (-sin^2 2x - cos^2 2x - 2sin 2x cos 2x + sin^2 2x + cos^2 2x + 2sin 2x cos 2x)/(cos 2x + sin 2x)^2
dy/dx = 0/(cos 2x + sin 2x)^2
Therefore, dy/dx = 0.