Difference quotient calculator with steps

Difference quotient calculator


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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
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)). 

Difference Quotient

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) = 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) = 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)
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