Given: \( y = \frac{\cos x - \sin x}{\cos x + \sin x} \)

Divide both numerator and denominator by \( \cos x \):

\( y = \frac{1 - \tan x}{1 + \tan x} \)

Recognize the tangent subtraction formula: \( \tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} \)

Here, \( A = \frac{\pi}{4} \) and \( B = x \), since \( \tan(\frac{\pi}{4}) = 1 \)

So, \( y = \tan(\frac{\pi}{4} - x) \)

Now, differentiate \( y \) with respect to \( x \):

\( \frac{dy}{dx} = \frac{d}{dx} \tan(\frac{\pi}{4} - x) \)

\( \frac{dy}{dx} = \sec^2(\frac{\pi}{4} - x) \cdot \frac{d}{dx}(\frac{\pi}{4} - x) \)

\( \frac{dy}{dx} = \sec^2(\frac{\pi}{4} - x) \cdot (-1) \)

\( \frac{dy}{dx} = -\sec^2(\frac{\pi}{4} - x) \)