# Difference Quotient Calculator



A step by step difference quotient calculator is presented.

## Difference Quotient Definition

Let $f(x)$ be a function and point $A(x,f(x))$ and $B(x+h,f(x+h))$ on the graph of $f$ as shown below.

The difference quotient of $f(x)$ is defined by:
$m = \dfrac{f(x+h)-f(x)}{h}$
which is the slope of the seacant line through the points $A$ and $B$.
The limit as $h$ approaches zero of the difference quotient, defined above, gives the important concept of the derivative of a function.

## Use of the Difference Quotient Calculator

1 - Enter and edit function $f(x)$ and click "Enter Function" then check what you have entered.
Note that the five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = x^3 + 1/x.(more notes on editing functions are located below)
2 - Click "Calculate Quotient".
3 - Note that the final expression of the difference quotient is simplified for polynomial and rational functions.
4 - The use of the present calculator and the definition of the derivative will help fully learn how to calculate derivative of a function using its definition.

$f(x)$ =

Notes: In editing functions, use the following:
1 - The five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example:    f(x) = x^2 + 1/x + log(x)  )
2 - The function square root function is written as (sqrt). (example: sqrt(x^2-1) for $\sqrt {x^2 - 1}$ )
3 - The exponential function is written as exp(x). (Example: exp(x+2)    for    $e^{x+2}$ )
4 - The log base e function is written as log(x). (Example: log(x^2-2)    for    $\ln(x^2 - 2$ )
Here are some examples of functions that you may copy and paste to practice:
x^2       3 x^2 + 2x       1/x       1 / (x -2)       (x-2)/(x+3)
sin(2x+1)       exp(x -2)       tan(x)       (x-1)/(x+3)^2