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?