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# Difference Quotient Calculator

To use the Difference Quotient Calculator, enter the function, select the variable, and click calculate button

## Difference Quotient Calculator

Difference quotient calculator is used to calculate the rate of change of the given function. This difference quotient calculator provides a step-by-step solution for every reliable input.

## What is the Difference quotient?

In mathematics, the term **“difference quotient”** refers to an expression that represents the average rate of change of a function over a small interval. It is usual practice in calculus to approximate the derivative of a function, which denotes the instantaneous rate of change of a function at a specific position.

It is denoted by “**h**” or “**Ꙙx**” and its mathematical formula is represented as.

**Ꙙx = (f(x + h) - f(x)) / h**

Where,** **

**f(x)**= function of “**x**”**h**= interval size**x + h**= small increment in the input.

## How to calculate the difference quotient?

Here are a few examples to learn how to evaluate difference quotient.

**Example 1**

If `f(x) = 3y`

then calculate the difference quotient.^{2}-2x

**Solution**

**Step 1:** Take the given function.

`f(x) = −2x+3y`

^{2}

**Step 2:** Write the formula of the Difference Quotient.

**Ꙙx = (f(x + h) - f(x)) / h**

**Step 3:** Now, put “`x = x + h`

” in **f(x)**.

f(x+h)= −2(x + h) + 3y^{2}

`f(x+h)= −2x - 2h + 3y`

^{2}

**Step 4:** Put the values **f(x)** and** f(x+h) **in the formula.

Ꙙx =[−2x - 2h + 3y^{2}] - [−2x+3y^{2}]/ h

Ꙙx = −2x - 2h + 3y^{2} + 2x - 3y^{2}/ h

Ꙙx = - 2h/ h

`Ꙙx = - 2`

Hence, **Ꙙx = - 2**, the difference quotient of “**f(x) = 3y ^{2}-2x**”.

**Example 2**

If `f(x) = 3x + 1 `

then calculate the difference quotient.

**Solution**

**Step 1:** Take the given function.

`f(x) = 3x + 1`

**Step 2:** Write the formula of the Difference Quotient.

**Ꙙx = (f(x + h) - f(x)) / h**

**Step 3:** Now, put “**x = x + h**” in **f(x)**.

f(x+h)= 3(x + h) + 1

`f(x+h)= 3x + 3h + 1`

**Step 4:** Put the values **f(x)** and** f(x+h)** in the formula.

Ꙙx =[3x + 3h + 1] - [3x + 1]/ h

Ꙙx = 3x + 3h + 1 - 3x - 1/ h

Ꙙx = 3h/ h

`Ꙙx = 3`

Hence, **Ꙙx = 3**, the difference quotient of “**f(x) = 3x + 1**”.