The quotient rule is a differentiation rule used to find the derivative of the ratio of two functions. Specifically, if you have a function of the form:

$f(x) = \frac{g(x)}{h(x)}$

where $g(x)$ and $h(x)$ are differentiable functions, the quotient rule states that the derivative of $f(x)$ is:

$f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{[h(x)]^2}$

Conditions for using the quotient rule:

1. Differentiability: Both $g(x)$ and $h(x)$ must be differentiable functions in the domain of interest. This means that both functions have derivatives.
2. Non-zero Denominator: The denominator function, $h(x)$, must not be equal to zero at the point where you are taking the derivative. Division by zero is undefined, so $h(x) \neq 0$.

Would you like a detailed example of how the quotient rule is applied, or do you have any specific questions about it?

Here are five related questions you might find helpful:

1. How do I apply the quotient rule to a specific function?
2. What is the product rule, and how does it differ from the quotient rule?
3. Can the quotient rule be simplified in some cases?
4. What happens if $h(x) = 0$ at some point in the domain?
5. How does the quotient rule extend to functions involving trigonometric functions?

Tip: When applying the quotient rule, always double-check the signs in the numerator, as they can sometimes lead to mistakes when dealing with subtraction.