Properties of the Quotient Rule

I. For $u(x)=\cos(x)$ and $v(x)=x$, the derivative of $\frac{\cos(x)}{x}$ computed using the quotient rule is $\frac{x*(-\sin(x))-\cos(x)}{x^2}$.

II. The quotient rule can be derived by rewriting the quotient as a product with the reciprocal of the denominator.

III. The quotient rule fails when the denominator is never zero.

Which of these statements is/are true concerning the quotient rule?