**Differentiation** is one of the important elements in the field of **Calculus**. It is the process to find derivatives of a function. **Microsoft Excel** has made our way easy to do** differentiation** for numerous functions instead of handwritten calculations. In this article, we will learn how to do **differentiation** in excel with some easy steps. Letâ€™s see how it works.

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## Download Workbook

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## Definition of Differentiation

In general, the term **differentiation** means the rate of change between two individual quantities or values. The ratio of the small change in one value is dependent on the first value given in the function. The basic formula for differentiation is** dy/dx**, where **y=f(x)**.

## Differential vs. Derivative

**Differential** and **Derivative **are two intimately connected terms in calculus. The term **derivative **means the rate of change of one variable with respect to another one. Here, **variables** are the changing entities.

On the other hand, the equation defining the relationship between the variables and derivatives is called the** differential equation**. It is basically the actual change of the function.

**Read More:** **How to Calculate Derivative from Data Points in Excel**

## Rules of Differentiation

When a differentiation point is **0**, then the function remains continuous. Otherwise, for each interval of position, sets a new product relating to the values. For this, there are certain rules in differentiation which are given below:

**1. Constant Rule**: **d[C]/dx=0**

**2. Power Rule**: **dx^n/dx=nx^n-1**

**3. Product Rule**: **d[f(x)g(x)]/dx=fâ€™(x)g(x)+f(x)gâ€™(x)**

**4. Quotient Rule**:** d/dx[f(x)/g(x)]=[g(x)fâ€™(x)-f(x)gâ€™(x)]/[g(x)]^2**

**5. Chain Rule**: **d/dx[f(g(x))]=fâ€™(g(x))gâ€™(x)**

## Step by Step Procedures to Do Differentiation in Excel

For illustration, we will apply the **power rule of differentiation** in excel. Letâ€™s go through the following step-by-step procedure.

### Step 1: Insert Horizontal Axis Values

Initially, we will insert the values of the **x-axis**. You can insert any other value of your preference.

- First, insert the value of
**x**in the**cell range B5:B13**. - Make sure to put the starting point
**0**. - Along with it, insert the value of
**n**.

### Step 2: Find Vertical Axis Values

Now, we will calculate the value of **y** for each value of **x**. Here, we will use this function for calculation:

`y=x^n`

- First, insert this formula in
**cell C5**.

`=B5^$E$5`

- Next, hit
**Enter**. - Here, you will see the first output of
**y**.

- Following, use the
**AutoFill**tool to insert this formula in**cell range C6:C13**.

### Step 3: Calculate Differentiation

Finally, we will do the calculation of differentiation at this stage. Follow the steps below:

- First, insert this formula in
**cell D5**.

`=(C6-C5)/(B6-B5)`

Here, **dy** means the difference between the last value and the immediately previous value of the **column y**. A similar function goes for** dx **as well.

- Then, press
**Enter**. - Thatâ€™s it, you have done your first differentiation.

- Lastly, apply a similar procedure for each set of values and you will get your final result.

**Read More:** **How to Calculate Second Derivative in Excel (2 Suitable Examples)**

### Step 4: Prepare Differentiation Graph

To visually represent the data, we will create a graph now. Follow the steps below:

- In the beginning, select
**cell range B4:B13**and**D4:D13**.

- After this, go to the
**Insert**tab and click on the**Scatter**chart under the**Charts**group.

- Following, select
**Scatter with Smooth Lines and Markers**chart type from the options.

- Thatâ€™s it, you have your initial graph based on the
**differential value vs. value of x**.

- After some modification, the final output looks like this:

**Read More:** **How to Make First Derivative Graph on Excel (With Easy Steps)**

## Example: Calculate Velocity with Differentiation in Excel

Let us see an example of differentiation. Here, we will calculate velocity based on certain values of time and distance. Follow the steps below:

- In the beginning, insert the value of
**time**and**distance**in**columns B**and**C**respectively.

- Then, insert this formula in
**cell D6**to calculate**delta t**.

`=B6-B5`

- Then, press
**Enter**. - Following, drag the bottom corner of
**cell D7**up to**cell D13**to find all values at once.

- Next, insert this formula in
**cell E6**.

`=C6-C5`

- Next, hit
**Enter**. - Following, use the
**AutoFill**tool to drag this formula in**cell range E7:E13**.

- Lastly, insert this formula in
**cell F6**.

`=E6/D6`

- As per above, apply this formula all over the
**cell F7:F13**.

- Finally, we have our values of velocity with differentiation calculation.
- Along with it, you can create a graph like this:

**Note**: As the

**time**and

**distance**are always

**0**in the beginning, therefore the initial value of velocity is

**0**as well.

## Things to Remember

- The constant value of differentiation is always
**0**in the**power rule**. - Make sure to insert a starting point. Otherwise, it will not show the proper result.

## Conclusion

Henceforth, thatâ€™s all for today. I hope it was a helpful article for you on how to do differentiation in excel with easy steps. Go through the procedures carefully and let us know your feedback. Follow **ExcelDemy** for more excel blogs.