If `y=(sinx)/(x+cosx)`, then find `(dy)/(dx)`.

Explanation

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

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

where \( u = \sin x \) and \( v = x + \cos x \).

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