# Difference quotient calculator with steps

## Difference quotient calculator

f(x)=

Solve for:

Are you struggling with finding the Difference quotient of a mathematical expression? Look no further! Our Difference quotient calculator with steps is here to help. With this tool, calculating the Difference quotient for any given function is just a few clicks away.

To use the calculator, simply follow these three easy steps:

1. Input the mathematical expression in the provided text field.
2. Select the variable for which you wish to calculate the Difference quotient.
3. Click the “Calculate” button. Once you do, a window will appear with a step-by-step explanation of the solution.

It’s that easy! Start using our Difference quotient calculator today and make your mathematical calculations a breeze.

## What is the difference quotient?

The difference quotient for the function f is given by the expression
f(x+h)−f(x)h
The difference quotient formula

The difference quotient is a mathematical concept used to measure the rate of change of a function f(x) with respect to x over a given interval [x, x+h]. It is calculated by finding the slope of the secant line that intersects the curve y=f(x) at two points: (x, f(x)) and (x+h, f(x+h)).

## How to find the difference quotient

Next we will show you how to find the difference quotient using an example generated with the help of our Difference quotient calculator:

Find the difference quotient for f(x) = xx+3

The difference quotient is given by

f(x+h)−f(x)h e.1

To find f(x+h), plug x + h instead of x:

f(x+h) = x+h(x+h)+3

Finally we substitute the values of f(x+h) and f(x) into e.1:

f(x+h)−f(x)h = x+h(x+h)+3xx+3 h

f(x+h)−f(x)h = 3(x+3+h)·(x+3)

## The difference quotient examples

Example 01: difference quotient of 1/x

f(x) = 1x

f(x+h)−f(x)h

f(x+h) = 1x+h

f(x+h)−f(x)h = 1x+h1x h

f(x+h)−f(x)h = −1x·(x+h)

Example 02: difference quotient of x2/(x2+3x)

f(x) = xx2+3·x

f(x+h)−f(x)h
f(x+h) = x+h(x+h)2+3·(x+h)

f(x+h)−f(x)h = x+h(x+h)2+3·(x+h)xx2+3·x h

f(x+h)−f(x)h = −1(x+3+h)·(x+3)