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Total Differential Calculator + Online Solver With Free Steps
The Total Differential Calculator is an online free tool that helps you to calculate the total differential of any given function. It finds the partial derivatives for the x and y with respect to z and adds them.
The calculator returns the total differential of the function as implicit derivatives of x and y with respect to x, y, and z.
What Is the Total Differential Calculator?
The total differential calculator is an online calculator that finds the total differential of a given function with respect to the provided variables.
Total Differential is an effective and helpful term used in Mathematics, specifically in Ordinary Differential Equations and calculus. It helps to find and approximate unknown values.
For example, if there is a triangle and you only know the length of its hypotenuse and one side. If you wish to find the length of the unknown side of that triangle, then you can use the total differential method to estimate the length of the third side of the triangle.
Usually, you can solve the total differentials by hand, but it is sometimes a complex and time-consuming process. The complexity increases as the functions become complicated, and you will have to find the partial derivatives individually.
The process of finding the derivatives in itself is a time taking approach. So, in a nutshell, finding Total Differentials manually can lead you to many problems.
Therefore, we offer you this simple Total Difference Calculator that quickly calculates the Total Differentials for any given function. It gives you multiple differentials for the given function.
This Total Differential calculator makes your work very easy and simple. You can perform your work much quicker and easier than the conventional method. This excellent calculator can perform several complex calculations in a few seconds.
This calculator is totally free of cost and very easy to use. You can access this calculator any time, anywhere. This is a ready-to-use tool, you need not perform any prior installations, downloading, or purchases before its usage.
It gives 100% accurate results within seconds. Its window is designed to be user-friendly and simple. You need to enter the required information, and your, results will be just a single click away.
This tool is specifically helpful for mathematics students working on differential equations who want to calculate the total differentials of functions.
In the upcoming sections of this article, you will find the procedure and a detailed explanation of the calculator. Keep reading for the best experience.
How To Use the Total Differential Calculator?
You can use the Total Differential Calculator by providing the function whose total differential needs to be calculated; all you need to do is to enter the values and click a button, the results will be displayed within a few seconds.
The calculator’s interface is designed to be very attractive, simple, and to the point so that anyone who uses it can comfortably use it even if he is experiencing it for the first time.
Anyone with some basic information regarding differential equations can easily use this calculator. The procedure to use this calculator is elaborated in detail below. You need to follow each of the given steps to get the results without error.
Step 1
Enter the function in the box labeled as “z=.” The function must be entered properly, and all the arithmetic tools should be entered with the keyboard.
Step 2
Now, click the Submit button. This will start the calculation of results.
Result
Once you click the submit button, a window pops up. This window consists of two sections. The first section shows the input function. The second section shows the output. This section consists of the partial derivatives of the function.
How Does the Total Differential Calculator Work?
The Total Differential Calculator works by calculating the total differential of the given function. The total differential is determined by finding the partial derivatives of the given function’s terms.
This calculator’s understanding will be clearer when there is knowledge about the following basic concepts.
What Is Differential Equation?
The differential equation is a mathematical equation with one more term and the derivatives of dependent variables concerning the independent variables. The derivatives can be partial derivatives or ordinary derivatives.
A differential equation basically represents the relationship between the quantity changing continuously concerning the variation in other quantities.
What Is a Derivative?
A derivative is the rate of change of a function at a point. Derivative measures the slope of the function. It is one of the fundamentals of calculus that is used in solving problems.
For example,
f(x) = dy/dx
Here x is the independent and y is the dependent variable.
What Are the Total Differentials?
The Total Differential of a function is the sum of all the independent variables with the partial derivatives of all the terms of the function concerning the variable times the total differential of that variable.
Formulae for Total Differentials
The formula for total differential depends on the number of variables and what the variables are. Following are examples of some basic formulas:
Function
f(x,y)
Total Differential
df = fxdx + fydy
Function
f(x, y, z)
Total Differential
df = fxdx + fydy + fzdz
Function
f(v, w, x, y, z)
Total differential
df = fvdv + fwdw + fxdx + fydy + fzdz
Solved Examples
A better way to comprehend the calculator’s functioning is to solve some examples using it and analyze those examples.
A few solved examples are given below that will help you to have a better understanding.
Example 1
Find the total differential for the following equation:
Solution
The calculator first calculates the partial derivative of x w.r.t z as:
∂x(y, z)/∂z = 1/2x
Now, it calculates the partial derivative of x w.r.t y
∂x(y, z)/∂y = -y/x
Now, it calculator partial derivative of y w.r.t z
∂y(x, z)/∂z = 1/2y
It calculates the partial derivative of y w.r.t x
∂y(x, z)/∂x = -x/y
Now, it calculates the partial derivative of z w.r.t y
∂z(x, y)/∂y = 2y
Finally, it calculates the partial derivative of z w.r.t x
∂z(x, y)/∂x = 2x