Find the derivative of `tan^(-1)((cosx - sinx)/(cosx + sinx))` with respect to 'x'

Explanation

To find the derivative of \( y = \tan^{-1}\left(\frac{\cos x - \sin x}{\cos x + \sin x}\right) \) with respect to \( x \), we can follow these steps:

### Step 1: Rewrite the Argument
We start with the expression inside the inverse tangent function:
\[ y = \tan^{-1}\left(\frac{\cos x - \sin x}{\cos x + \sin x}\right) \]
We can simplify this expression by recognizing that it can be represented as a tangent of an angle. We divide both the numerator and the denominator by \( \cos x \):
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