Looking for ways to know how to calculate the second derivative in Excel? We use the second derivative of a function for different purposes in our day-to-day life. Here, you will find 2 ways to calculate the second derivative in Excel.

## How to Calculate Second Derivative in Excel: 2 Examples

Here, you will find how to calculate the second derivative of a function by manually calculating and using Scatter Plot.

### 1. Manually Calculating Second Derivative

In the first method, we will show you how to calculate the second derivative of a function Manually.

Here, we have a function of x. The equation of the function is given below.

`f(x)= sin(x^2)+10 `

The **1st derivative** of the function,

`f’(x)= 2xcox(x^2)`

Finally, the **2nd derivative** of the function,

`f’’(x)= 2cos(x^2)-4x^2sin(x^2)`

The dataset provides some values of **x**. Now, we will show you how to manually calculate the second derivative for these values of **x**.

Follow the steps given below to do it on your own.

**Steps:**

- Firstly, select Cell
**C5**. - Then, insert the following formula.

`=2*COS(B5^2)-4*B5*B5*SIN(B5^2)`

Here, in the formula, we inserted Cell **B5 **as **x**.

- Now, press
**ENTER**. - After that, drag down the
**Fill Handle**tool to AutoFill the formula for the rest of the cells.

- Finally, you will get all the values of the second derivative of the function by calculating manually.

### 2. Using Scatter Plot to Calculate 2nd Derivative

We can also calculate the second derivative using **Scatter Plot **in Excel.

Here, we have a function of x. The equation of the function is given below.

`f(x)= 2x^2+x`

The **1st derivative** of the function,

`f’(x)= 4x+1`

The dataset provides some values of **x**. Now, we will show you how to calculate the second derivative for these values of **x** using **Scatter Plot**.

__Step-01:__ Calculating First Derivative

Firstly, we will show you how to calculate the first derivative of the function in Excel. Go through the steps given below to do it on your own.

- In the beginning, select Cell
**C5**. - Then, insert the following formula.

`=4*B5+1`

Here, in the formula, we inserted Cell **B5 **as **x**.

- Now, press
**ENTER**. - After that, drag down the
**Fill Handle**tool to AutoFill the formula for the rest of the cells.

- Finally, you will get all the values of the first derivative of the function.

__Step-02:__ Inserting Scatter Plot

Now, we will show you how to **insert **a **scatter plot **in Excel to calculate the second derivative of a function. Follow the steps given below to do it on your own.

- Firstly, select Cell range
**B4:C11**. - After that, go to the
**Insert tab**>> click on**Insert Scatter or Bubble Chart**>> select**Scatter**.

- Now, a
**Scatter Plot**will be inserted. - Then, click on the
**“+”**sign to open**Chart Elements**. - Next, turn on
**Axis Titles**.

- After that, select the
**x-axis Title**and type**x**.

- Then, select the
**x**. - Now, select
**Font Size**as**14**and click on**Bold**.

- Similarly, change the
**y-axis****Title**as**f’(x)**and format it.

- Next, select the
**Chart Title**.

- After that, type
**Determining f’’(x)**as the**Chart Title**.

- Then, click on the
**“+”**sign to open**Chart Elements**. - Next, click on
**Trendline**>> select**More Options**.

- Now, the
**Format Trendline**box will open. - After that, select the
**Display Equation on chart**option.

- Again, click on the
**“+”**sign to open**Chart Elements**. - Next, turn off
**Gridlines**to clearly see the equation.

- Then, select the
**equation**. - After that, set
**14**as**Font Size**and click on**Bold**.

Here, we get **y= 4x+1** as the equation of the Trendline.

Now, if we compare the equation with** y= mx+c**, we get** m=4 **which is the **slope **of the graph. We know that the **slope **of the **1st derivative** and value of **x **of a function is equal to its second derivative. So, from the **scatter plot**, we get **4 **as the **second derivative** of the function.

__Step-03:__ Cross-Checking Value of Second Derivative Using SLOPE Function

Finally, we will show how to cross-check the value of the second derivative of a function using **the SLOPE Function**. Go through the steps given below to do it on your own.

- Firstly, select Cell
**C15**. - Then, insert the following formula.

`=SLOPE(C5:C11,B5:B11)`

Here, in the **SLOPE Function**, we used Cell range **C5:C11** as **known_ys **and Cell range **B5:B11** as **known_xs**.

- After that, press
**ENTER**.

- Finally, you will get the value of the
**Slope**using the**SLOPE Function**.

Now, you can see that the value of the **slope **is **4**. So, the value of the **second derivative **of this function is **4**.

## Practice Section

In this section, we are giving you the dataset to practice on your own and learn to use these methods.

**Download Practice Workbook**

## Conclusion

So, in this article, you will find 2 ways to calculate the second derivative in Excel. Use any of these ways to accomplish the result in this regard. Hope you find this article helpful and informative. Feel free to comment if something seems difficult to understand. Let us know any other approaches which we might have missed here.

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