# Quotient rule review

Review your knowledge of the Quotient rule for derivatives, and use it to solve problems.

## What is the Quotient rule?

The Quotient rule tells us how to differentiate expressions that are the quotient of two other, more basic, expressions:

Basically, you take the derivative of $f$ multiplied by $g$, subtract $f$ multiplied by the derivative of $g$, and divide all that by $[g(x)]^2$.

*Want to learn more about the Quotient rule? Check out this video.*

## What problems can I solve with the Quotient rule?

### Example 1

Consider the following differentiation of $\dfrac{\sin(x)}{x^2}$:

### Check your understanding

*Want to try more problems like this? Check out this exercise.*

### Example 2

Suppose we are given this table of values:

$x$ | $f(x)$ | $g(x)$ | $f'(x)$ | $g'(x)$ |
---|---|---|---|---|

$4$ | $-4$ | $-2$ | $0$ | $8$ |

$H(x)$ is defined as $\dfrac{f(x)}{g(x)}$, and we are asked to find $H'(4)$.

The Quotient rule tells us that $H'(x)$ is $\dfrac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}$. This means $H'(4)$ is $\dfrac{f'(4)g(4)-f(4)g'(4)}{[g(4)]^2}$. Now let's plug the values from the table in the expression:

### Check your understanding

*Want to try more problems like this? Check out this exercise.*