Difference between partial and total derivative | Partial derivative equations

Difference between partial and total derivative | Partial derivative equations | Total derivative

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What is the difference between partial derivative and total derivative? In this video, I have explained what is a partial derivative and total derivative. I have furst shown the similarity between partial derivative and total derivative. Then, I have explained using a cube what is the difference between partial derivative and total derivative. I have also provided provided examples using values, showing the difference between partial derivative and total derivative and using a function I have demonstrated and explained the same.
00:00 - 01:04 - Introduction
01:05 - 02:25 - What is partial and total derivative?
02:26 - 04:22 - What are the similarities?
04:23 - 08:16 - Difference between partial and total derivative
08:17 - 12:32 - Example using a cube
12:33 - 15:41 - Example using a function
15:42 - 16:30 - Summary
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Пікірлер: 16

@jonathondelemos4609 11 ай бұрын

This is a really good explanation. Partials signify one variables rate of change. An application of this could be the rate of change of heat within a machine apparatus. If taking the partial of a heat variable shows dangerous rates of change, we know the apparatus is unsafe. This is different that muddying the data by showing the rate of change of potentially countless variables.

@physicsforstudents 11 ай бұрын

You have aptly defined the rate of change using the example of machine apparatus. Thank you for that. I am happy that you have enjoyed this video. Thanks. Please do share and like and keep an eye as more such interesting stuffs are coming up. Thank you.

@abhirupmoitra8711 11 ай бұрын

I have already seen that video. I would like to give a big round of applause. You always provide lucid explanation of abstract mathematical concepts and it inspires me a lot. Sometimes I take notes of your explanations. Trust me my friends, and teachers appreciate my learning skills. And credit goes to you.

@physicsforstudents 11 ай бұрын

Thanks and a lot of appreciation

@youcan7255 10 ай бұрын

Nice sir . I am from nepal ❤

@physicsforstudents 10 ай бұрын

Thanks and welcome. For any doubt, feel free to contact.

@youcan7255 10 ай бұрын

@@physicsforstudents huss sir . Sir plz lunch full series of calculus🙏🙏

@MrThayumanavan Жыл бұрын

Sir, Is there partial and total integration on similar lines?

@physicsforstudents Жыл бұрын

Sorry for the late reply. No, partial and total integration are not the same as partial derivative and total derivative. Partial integration refers to the process of integrating a function with respect to one variable while treating the other variables as constants. It is often used in multivariable calculus and is related to finding antiderivatives in multiple dimensions. The result is a function of the remaining variables. On the other hand, partial derivatives involve finding the rate at which a function changes with respect to one variable while holding the other variables constant. It measures the sensitivity of the function to changes in a particular variable. Total integration is not a commonly used term in mathematics. However, if you meant the definite integral, it refers to finding the area under a curve or the accumulation of a quantity over an interval. The definite integral can be seen as the limit of a sum of infinitely many infinitesimally small areas. Total derivative, on the other hand, refers to the derivative of a function with respect to a variable, taking into account the dependence of the function on all its variables. It generalizes the concept of differentiation to multivariable functions.

@ij_bind Жыл бұрын

Best clarification,thank you sir

@physicsforstudents Жыл бұрын

@@ij_bindThank you !!

@MrThayumanavan Жыл бұрын

Thanks for your clarification. Can it be concluded that the partial derivatives can't be integrated to get back the original function? I am trying to get your views so that I may guide my grandsons who are just getting exposure to Calculus.

@physicsforstudents Жыл бұрын

@@MrThayumanavan In general, it is true that integrating the partial derivatives of a function does not guarantee that you will obtain the original function. This is because partial derivatives only tell you how a function changes with respect to one variable, while integration tells you the total change in a function over a range of values. To illustrate this point, let's consider a simple example. Suppose we have a function f(x, y) that depends on two variables x and y. If we differentiate this function partially with respect to x, we obtain the partial derivative ∂f/∂x. Similarly, if we differentiate f(x, y) partially with respect to y, we get the partial derivative ∂f/∂y. If we integrate ∂f/∂x with respect to x, we obtain a new function g(x, y). Similarly, integrating ∂f/∂y with respect to y gives us another function h(x, y). However, there is no guarantee that g(x, y) or h(x, y) will be the same as the original function f(x, y). In fact, integrating the partial derivatives independently may introduce additional constants of integration, which can lead to different functions. There are some special cases where partial derivatives can be integrated to get back the original function. For example, if f(x,y) is a linear function of x and y, then its partial derivatives are constant, and the integral of a constant is simply the constant itself. However, in general, partial derivatives cannot be integrated to get back the original function. I am planning to start a fresh new course on Calculus.

@ditch3827 Жыл бұрын

@physicsforstudents Жыл бұрын

You set out to explain the difference between curly dA / curly dl and dA/dl but then go on to explain the difference curly dA / curly dl and dA, but not dA/dl, so the question was not answered. Or did I miss something? I have explained da/dl as the calculation for total derivative, the overall rate of change of the surface area with respect to the length, considering changes in all dimensions of the box. The da/dl is just meant to illustrate the concept of total derivative. In the video, further, there is no reference of da/dl but rather using a function, which gives the total derivative as df.