The quotient rule is used to find the derivative of a ratio between two functions. It is used in the case of tan(x) and cot(x) because tan(x) can be written as [tex]\frac{sin(x)}{cos(x)}[/tex] (so f(x) = tan(x) is really f(x) = [tex]\frac{sin(x)}{cos(x)}[/tex]). Similarly, cot(x) can be written as [tex]\frac{cos(x)}{sin(x)}[/tex], so the quotient rule also applies.
