The quotient rule is a method for finding the derivative of a function that is the ratio of two differentiable functions. The rule states that if two differentiable functions, f(x) and g(x), exist, then their quotient is also differentiable, and the derivative of the quotient of these two functions also exists. The formula for the quotient rule is:
$$\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{g(x)\cdot f(x)-f(x)\cdot g(x)}{[g(x)]^2}$$
where f(x) and g(x) are the derivatives of f(x) and g(x), respectively.
The quotient rule can be derived from other derivative rules, such as the product rule and the chain rule. It is a powerful technique for finding the derivative of a function expressed as a quotient.
