❖ General Chain Rule And Partial Derivatives ❖

📚 Mastering the Generalized Chain Rule in Multivariable Calculus: Examples and Diagrams 🧮
In this video, we dive into the Generalized Chain Rule, a powerful technique used in multivariable calculus to compute derivatives when multiple variables are involved. This is an essential concept for anyone studying calculus in higher dimensions, especially when dealing with composite functions of several variables. I’ll walk you through two detailed examples and use diagrams to help visualize how the partial derivatives fit together.
🚀 What you’ll learn:
How the Generalized Chain Rule extends the basic chain rule to functions of multiple variables.
Step-by-step solutions for applying the Generalized Chain Rule to two different examples.
How to use diagrams to map out relationships between variables and find the correct partial derivatives.
Clear explanations of partial derivatives and their role in multivariable calculus.
If you're studying multivariable calculus, preparing for Calculus III, or just want to deepen your understanding of advanced calculus topics, this video will give you the insights and practice you need. The use of diagrams will make it easier to grasp the connections between variables and functions.
For more in-depth calculus tutorials, be sure to check out my other videos on topics like gradient vectors, Lagrange multipliers, and more.
👍 Don’t forget to like, subscribe, and hit the notification bell for more advanced math tutorials! 🔔✨
Watch now to master the Generalized Chain Rule and take your multivariable calculus skills to the next level!
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@MajinAmmaar no, not exactly; i assume you are in first semester calculus, so you are still doing single variable stuff; this has to do with multivariable stuff. technically this applies to what you are doing, but the general power rule is a specific rule versus a general procedure (which this is)

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Hi Patrick, Your videos are just amazing and is helping me to re-learn some of the basics after almost 10 years of no contact with maths! Thanks. Could you please double check the end part as I'm a bit confused about some of the partial derivaties that you did (specially with constants)? maybe I'm confused...but any help would be great.

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[@commanderkool868]

@bfferz in the second example he uses the partial of x to u because x depends on more than one variable, in the first example x only depended upon t so the derivative was used rather than the partial

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The chain rule for normal functions is for calculus 1 but this is multivariable calculus (calc. 3 in my U) so its a different chain rule.

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glad you liked the video!

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[@adildudhia1878]

You should substitute your functions of x and y at the end. If you’re trying to find the derivative of z with respect to t, your final answer should be in terms of t, not x and y. Same goes for second example.

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