Calculus

Quotient Rule - Calculus

Learn the quotient rule with examples, step-by-step guide, and calculator tools. Differentiate quotient of two functions

The quotient rule is a fundamental concept in calculus. Differentiate quotient of two functions. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

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

Variables

f(x), g(x)
Functions
f'(x), g'(x)
Derivatives

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [] → d/dx[x/sin(x)] = (sin(x) - x cos(x)) / sin²(x)

Example 2

Example 2: (sin(x) - x cos(x)) / sin²(x)

Frequently Asked Questions

What is the quotient rule?

Differentiate quotient of two functions

How do I calculate quotient rule?

Use the formula: \frac{d}{dx}\left[\frac{f(x)}{g(x)}\right] = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}. Follow the steps provided above.

What tools can help with quotient rule?

We provide online calculators: calculator

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