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!

Discover the quotient rule formula used in calculus to differentiate functions that are the quotient of two differentiable functions. Learn how to apply the rule and understand its components with step-by-step explanations and related questions. Suitable for advanced high school and college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation