How to Do Calculus in Excel (Differentiation and Integration)

How to Calculate Differentiation Manually in Excel?

Steps:

Set the differentiation equation.

y= x²+7x+5

Dy/Dx = 2x+7

Use the differentiation results as a reference formula.
We have taken several x-values and their corresponding y-values. As we have the differential formula for our equation, we can find differentiation at every x-value.

Showing Dataset to find Differentiation

Enter the following formula in D8:

=2*B8+7

Press ENTER.
We get differentiation for the first point, which is -1.
Hold and drag cell D8 downwards to find differentiation for all points.

Showing Result after finding all Differentiations

Finding Differentiation by Formula

Steps:

The finite difference formula is given as:

f’(x)= {f(x+h)-f(x)}/h

Set the value of h and find f(x+h) and f(x). From these values, we will find the differentiation of (x). We have set the value of h as 0.0001.

Showing Dataset to find Differentiation with Formula

Enter the following formula in E8 to find the value of x+h.

=B8+$D$8

Hold and drag the E8 cell downwards to get all x+h values.

Finding x+h values

To find the values of f(x+h), enter the following formula in F8:

=E8^2+7*E8+5

Press ENTER.
Hold and drag the F8 cell downwards to find all f(x+h).

Finding F(x+h) Values

To find f’(x), enter the following formula in G8:

=(F8-C8)/$D$8

Press Enter.
Hold and drag the G8 cell downwards to find all f’(x).

Using manual formula to find Differentiations

Finding Integration in Excel

Calculating Integration Manually

Steps:

The integration of the equation is given as:

∫y.dx =x^3/3+(7x^2)/2+5x

Showing Dataset for Manual Integration

Enter the following formula in D8 and press ENTER.

=B8^3/3+(7*B8^2)/2+5*B8

Hold and drag the D8 cell downwards to find integration at all points.

Finding Integration with Manual Formula

Finding the Area under the Curve with Integration

Steps:

Enter the following formula in D8 and press ENTER.

=(B8-B7)*(C8-C7)/2

Hold and drag the D8 cell downwards to get all the interval areas.

Using Trapezoidal Formula to Calculate each Interval Area

To sum up all these area intervals, we will use the SUM function. Here is the overview of the SUM function:

Click the image for a detailed view

Use the following formula in D18:

=SUM(D8:D17)

Applying the SUM function to find total Area Under Curve

Finding a Derivative with the SLOPE function

The overview of the SLOPE function is given in the following image:

Click the image for a detailed view

Let’s find the average velocity with this in-built function.

Steps:

Enter the following formula in C14 and press ENTER.

=SLOPE(B5:B12,C5:C12)

You will get the average velocity, which is 4.74 ms^-1.

Using SLOPE Function to Find Derivative

Things Should You Remember

When finding an area under a curve, you should take as much interval as possible. The more intervals you take, the more accurate your result will be.
The result from these procedures is not cent percent accurate. Different methods may give you different results.
While differentiating with the finite difference method, you must take the value of h very small for more accuracy.
Be careful while using the formulas. Especially in the case of relative and absolute referencing.

Download the Practice Workbook

Performing Calculus.xlsx