How to Find Partial Derivatives in Excel (with Easy Steps)

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A partial derivative in mathematics is the function’s derivative with respect to one of the variables while keeping the others constant (as opposed to the total derivative, in which all variables are allowed to vary). In differential geometry and vector calculus, partial derivatives are used. This article will show you how to find partial derivatives in Excel using a very basic function.


How to Find Partial Derivatives in Excel: Easy Steps

In this article, we will demonstrate to you how to find partial derivatives in Excel by making equations using the Equation command from the Insert tab, and then we will determine the first and second derivatives for all the variables in the equation as well as their corresponding results.


Step 1. Utilizing Equation Command to Make Derivatives Equations

To write any mathematical equation in Excel, we have a dedicated command called “Equation.” We can almost write any equation in a mathematical form using the Equation command. To utilize the command, just follow the procedures below.

  • Firstly, go to the Insert tab.
  • Secondly, choose the Symbols tool.
  • Thirdly, click on the Equation command, and then you will make the desired equation that you want to work with.
  • Here, we will write an equation for determining the partial derivatives of X and Y variables.
  • So, the given equation is shown below.

Utilizing Equation Command to Make Partial Derivatives Equations in Excel


Step 2. Computing First Derivative for First Variable

We will calculate the first derivative with respect to the variable X in this section. In the image below, you will see the first derivative for the given function.

  • Here, we will calculate the first derivative with respect to variable X.

Computing First Derivative For First Variable to Find Partial Derivatives in Excel


Step 3. Computing Second Derivative for First Variable

Similar to Step 2, we will find the second derivative for the given function by using the following formula.

  • Then, we will evaluate the second derivative with respect to variable X.

Computing Second Derivative For First Variable to Find Partial Derivatives in Excel


Step 4. Computing First Derivative for Second Variable

In this section, we will calculate the first derivative with respect to the variable Y. The given image demonstrates to you the first derivative of the given function.

  • Here, we will calculate the first derivative with respect to variable Y.

Computing First Derivative For Second Variable Find Partial Derivatives in Excel


Step 5. Computing the Second Derivative for the Second Variable

In this part, we will determine the second derivatives for the variable Y by using the following formula for partial derivatives.

  • Then, we will evaluate the second derivative with respect to variable Y.

Computing Second Derivative For Second Variable to Find Partial Derivatives in Excel


Step 6. Showing Final Result

In the final section, we will simulate the partial derivatives in numerical form. To do that, we assign some values for X, Y, and n.

  • In this part, you will see the following formula for determining the result for the first derivatives of variable X.
=K6*(K4^(K6-1)*(K5^K6))
  • Then, press ENTER.

Showing Final Result to Find Partial Derivatives in Excel

  • Finally, the given image shows the result of the first derivatives of variable X.
  • After that, write down the following formula for the second derivatives.
=K6*(K6-1)*(K4^(K6-2)*(K5^K6))
  • Besides, hit ENTER.

  • Lastly, the given image shows the result of the first and second derivatives of variable X.

Showing Final Result to Find Partial Derivatives in Excel

  • After that, you will see the following formula for determining the result for the first derivatives of variable Y.
=K6*(K5^(K6-1)*(K4^K6))
  • Then press ENTER.

  • Therefore, the given image displays the result of the first derivatives of variable Y.
  • Then, write down the following formula for the second derivatives.
=K6*(K6-1)*(K5^(K6-2)*(K4^K6))
  • Besides, hit ENTER.

  • As a result,  the given image displays the result of the first and second derivatives of variable Y.


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Conclusion

In this article, we’ve covered step-by-step procedures to find partial derivatives in Excel. We sincerely hope you enjoyed and learned a lot from this article. If you have any questions, comments, or recommendations, kindly leave them in the comment section below.


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Bishawajit Chakraborty
Bishawajit Chakraborty

Bishawajit Chakraborty, a Rajshahi University of Engineering & Technology graduate with a B.Sc. in Mechanical Engineering, has been associated with ExcelDemy since 2022. Presently, he is a content developer, specializing in Excel Power Query, Data Analysis and VBA. It is worth mentioning that he has authored more than 90 articles on VBA content development. His profound interest lies in the fields of data analytics and data science. He possesses expertise in VBA, Power BI, machine learning, and Python... Read Full Bio

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