Introduction to Partial Derivative Calculator:
Partial derivative calculator with steps is an online tool that helps you to evaluate the function which has more than one variable for derivation in multivariable calculus. Our tool is used to find the differentiation with respect to one or two variables.
The partial differentiation calculator is a beneficial tool for students or teacher because when you deal with multivariable differentaition function you may get confused or stuck at a point where you cannot find its solution but our calculator gives you accurate solution even for complex partial derivative problems.
What is a Partial Derivative?
Partial derivative is define as a multivariable function where the derivation of function is takes with respect to one of its variables by keeping the other value as constant. It is a fundamental concept in which function depends on more than one variable of differentiation.
It is denoted with “∂f/∂x or fx or “∂-xf” partial symbol. This process is used in various fields like physics, economic, engineering or machine leaning. The formula behind the multivariable derivative calculator can be express mathmatically as:
$$ \frac{\partial f}{\partial x}(x_0, y_0, z_0, … ) \;=\; \lim_{\Delta x \to 0} \frac{f(x_0 + \Delta x, y_0, z_0, … ) - f(x_0, y_0, z_0, … )}{\Delta x} $$
How to Calculate Partial Derivative?
For the calculation of partial derivative of function, the partial derivative at a point calculator evaluate with respect to one variable while keeping all other variables as constants. Here is a step-by-step guide on how to calculate the partial derivative of a multivariable function.
Step 1:
Identify the Function f(x,y,z,…) and its variables that you want to differentiate.
Step 2:
Choose the Variable that you want to differentiate with respect to x.
Step 3:
Make sure to keep other variables as constants while differentiating with respect to x, keep all other variables (y,z,…) as constants.
Step 4:
Apply the standard rules of differentiation for partial derivative function with respect to the your chosen variable.
Solved Example of Partial Derivative:
The solved example of partial derivative will help you understand how the partial derivative calculator with steps solves the partial derivative problems easily.
Example: Determine ∂f/∂x and ∂f/∂y for the following,
$$ f(x,y) \;=\; x^2 - 3xy + 2y^2 - 4x + 5y - 12 $$
Solution:
To calculate ∂f/∂x, use the variable y as constant.
Apply sum, difference or power rule of derivative in the given function f(x).
$$ \frac{\partial f}{\partial x} \;=\; \frac{\partial }{\partial x} \left[x^2 - 3xy + 2y^2 - 4x + 5y - 12 \right] $$
$$ =\; \frac{\partial}{\partial x} [x^2] - \frac{\partial}{\partial x} [3xy] + \frac{\partial}{\partial x}[2y^2] - \frac{\partial}{\partial x} [4x] + \frac{\partial}{\partial x}[5y] - \frac{\partial}{\partial x}[12] $$
$$ =\; 2x - 3y + 0 - 4 + 0 - 0 $$
$$ =\; 2x - 3y - 4 $$
To calculate ∂f/∂y, treat the variable x as a constant.
$$ \frac{\partial f}{\partial y} \;=\; \frac{\partial}{\partial y}[x^2 - 3xy + 2y^2 - 4x + 5y - 12 ] $$
$$ =\; \frac{\partial}{\partial y}[x^2] - \frac{\partial}{\partial y}[3xy] + \frac{\partial}{\partial y}[2y^2] - \frac{\partial}{\partial y}[4x] + \frac{\partial}{\partial y}[5y] - \frac{\partial}{\partial y}[12] $$
$$ =\; -3x + 4y - 0 + 5 - 0 $$
$$ =\; -3x + 4y + 5 $$
How to Use Partial Derivative Calculator?
The partial differentiation calculator has an easy-to-use interface, so you can easily use it to evaluate the given partial differential function solution. Before adding the input value problems, you must follow some simple steps. These steps are:
- Enter the partial derivation function f(x) in the input field that you want to evaluate for multivariable function.
- Add the derivative variable on which your function is partial differentiated in the input field.
- Recheck your input value for the given partial derivative problem solution before hitting the calculate button to start the calculation process in the multivariable derivative calculator.
- Click on the “Calculate” button to get the desired result of your given partial derivative problem.
- If you want to try out our partial derivative at a point calculator to check its accuracy in solution, use the load example.
- Click on the “Recalculate” button to get a new page for solving more partial derivative questions with solution.
Final Result of Partial Differentiation Calculator:
Partial derivative Calculator with steps gives you the solution to a given derivative problem when you add the input value to it. It provides you with solutions that may contain as:
- Result Option:
You can click on the result option as it provides you with a solution to partial derivative questions.
- Possible Step:
When you click on the possible steps option then the multi derivative calculator provides you with the solution of the partial differential problem in step.
- Plot option:
Plot option provides you solution in form of graph for visual understanding of partial derivative function.
Advantages of Multivariable Derivative Calculator:
The partial differentiation calculator gives you multiple advantages whenever you use it to calculate partial derivation problems to get its solution. These advantages are:
- You just add your function in this partial derivative at a point calculator and you get solution even it is for complicated partial derivation function.
- It is a free-of-cost tool that provides you a solution for a given partial derivation function to find the multivariable differentiation using the differential rules without spending.
- Our Calculator saves the time and effort that you consume in solving partial differential questions to get solutions in a few seconds.
- It is an adaptive tool that allows you to find the different type of multivariable derivation.
- Multi derivative calculator will give you results when you are computing partial differentiation function easily without taking any asistance but in manual calculation there is a high chances of mistakes increasing.
- You can use this tool for practice you will get familiar with the concept of partial derivative function.
- Partial derivative Calculator with steps is a trustworthy tool that provides you with correct solutions as per your input to calculate the partial derivative problem.
