Difference Quotient Calculator

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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.
difference quotient definition
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



More References and Links

Difference Quotient
Derivative Definition
derivative
rules
formulas

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