Find the differential coefficient of `(sin x -x cos x)/(x sin x+cos x)` with respect to x.

Explanation

To find the differential coefficient of the function \( y = \frac{\sin x - x \cos x}{x \sin x + \cos x} \) with respect to \( x \), we will use the quotient rule for differentiation. The quotient rule states that if you have a function \( y = \frac{u}{v} \), then the derivative \( \frac{dy}{dx} \) is given by:

\[ \frac{dy}{dx} = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} \]

where \( u \) is the numerator and \( v \) is the denominator.

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