The quotient rule is a formula used in calculus for finding the derivative of a function that is the quotient of two differentiable functions. If we have a function $f(x) = \frac{g(x)}{h(x)}$, where both $g(x)$ and $h(x)$ are differentiable, the quotient rule states:

$\frac{d}{dx} \left( \frac{g(x)}{h(x)} \right) = \frac{h(x) g'(x) - g(x) h'(x)}{[h(x)]^2}$

Where:

• $g(x)$ is the numerator function,
• $h(x)$ is the denominator function,
• $g'(x)$ is the derivative of $g(x)$,
• $h'(x)$ is the derivative of $h(x)$.

Would you like a detailed explanation or an example?

Here are 5 related questions to deepen your understanding:

1. How does the quotient rule compare to the product rule?
2. Can the quotient rule be applied to more complex functions like trigonometric or exponential ones?
3. How is the quotient rule derived from the product and chain rules?
4. What happens when the denominator $h(x)$ approaches zero?
5. Can the quotient rule be simplified for certain types of functions?

Tip: To avoid mistakes, always simplify your functions as much as possible before applying the quotient rule!