In these lessons, we shall learn to find the derivative using the quotient rule.

**Related Pages**

Calculus: Derivatives

Calculus: Power Rule

Calculus: Product Rule

Calculus: Chain Rule

Calculus Lessons

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:**

**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.

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