The quotient rule is a method for finding the derivative of a function that is the ratio of two differentiable functions. The rule is used in calculus to differentiate problems where one function is divided by another. The formula for the quotient rule is as follows: 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 is given by the formula:
$$\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{g(x)f(x)-f(x)g(x)}{[g(x)]^2}$$
where f(x) and g(x) are the derivatives of f(x) and g(x), respectively. The quotient rule can be derived using other derivative rules, such as the product rule. It is important to note that the quotient rule is not always necessary, and the power rule can be used instead. However, the chain rule is required to use the power rule, so it is often best to stick with the quotient rule until the chain rule is learned.
