Spiegare gentilmente i ragionamenti, i passaggi e argomentare.
$ D(y(x)) = D(3) + D(ln\,tan(\pi - \frac{x}{2})) $
$ D(y(x)) = \frac{1}{tan(\pi - \frac{x}{2})} D(tan(\pi - \frac{x}{2})) $
$ D(y(x)) = \frac{cos(\pi - \frac{x}{2})}{sin(\pi - \frac{x}{2})} \frac{1}{cos^2(\pi - \frac{x}{2})} D(\pi - \frac{x}{2}) $
$ D(y(x)) = \frac{1}{sin(\pi - \frac{x}{2})cos(\pi - \frac{x}{2})} (- \frac{1}{2}) $
$ D(y(x)) = - \frac{1}{2 sin(\pi - \frac{x}{2})cos(\pi - \frac{x}{2})} $
$ D(y(x)) = - \frac{1}{sin(2(\pi - \frac{x}{2})} $
$ D(y(x)) = - \frac{1}{sin(2\pi - x)} $
$ D(y(x)) = - \frac{1}{sin(- x)} $
$ D(y(x)) = \frac{1}{sinx} $