Introduction to Partial Derivative Calculator:
Partial derivative calculator with steps is an online tool that helps 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 more variables.
The partial differentiation calculator is a beneficial tool for students or teacher as it deals with multivariable differentaition function and gives you accurate solution even for complex partial derivative problems.
What is a Partial Derivative?
Partial derivative is defined as a multivariable function 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 expressed 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?
In multivariable calculus, partial derivatives are important to understand the change in functions with respect to individual variables, taking others as constant. This concept is useful for analyzing multiple functions, as in calculation of Wronskian, a determinant helps determine the linear independence of a set of functions. By calculating partial derivatives, we learn behaviour of each 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 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. Before adding the input value problems, you must follow some simple steps that 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 of multivariable derivative calculator to start the calculation process.
- Click on the “Calculate” button to get the desired result of your given partial derivative problem.
- If you want to try our partial derivative at a point calculator to check its accuracy in solution, use the load example option.
- Click on the “Recalculate” button to get a new page for solving more partial derivative questions.
Final Result of Partial Differentiation Calculator:
Partial derivative calculator with steps gives you the solution of derivative problem when you give it an input. It provides you solutions that 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 step by step solution of the partial differential problem.
- 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. These advantages are:
- You just add your function in this partial derivative at a point calculator and you get solution even it is complicated partial derivation function.
- It is a free-of-cost tool that provides you a solution of partial derivation function and to find the multivariable differentiation using the differential rules for free.
- Our calculator saves the time and effort that you consume in solving partial differential questions to get solutions.
- It is an adaptive tool that allows you to find the different type of multivariable derivation.
- Multi derivative calculator compute partial differentiation function easily without any mistake but in manual calculation there is a high chances of mistakes.
- You can use this tool for practicing and you will get familiarity 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.
