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The quotient rule is used to find the derivative of the division of two functions.

### The Quotient Rule

**Why the quotient rule is the same thing as the product rule?**

Introduction to the derivative of e^{x}, ln x, sin x, cos x, and tan x.
**Calculus: Quotient Rule and Simplifying**

The quotient rule is useful when trying to find the derivative of a function that is divided by another function. As long as both functions have derivatives, the quotient rule tells us that the final derivative is a specific combination of both of the original functions and their derivatives.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Calculus

Math Worksheets

The quotient rule is used to find the derivative of the division of two functions.

The quotient rule says that the derivative of the quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

The following diagrams show the Quotient Rule used to find the derivative of the division of two functions. Scroll down the page for more examples and solutions on how to use the Quotient Rule.If *f* and *g* are differentiable, then

**Example:**

Given that , find *f* ‘(*x*)

**Solution:**

**Example:**

Given that , find *f* ‘(*x*)

**Solution:**

Introduction to the derivative of e

The quotient rule is useful when trying to find the derivative of a function that is divided by another function. As long as both functions have derivatives, the quotient rule tells us that the final derivative is a specific combination of both of the original functions and their derivatives.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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