Solving Lagrangian Derivation - Classical Mechanics by John R. Taylor

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The discussion revolves around a derivation in "Lagrangian from Classical Mechanics" by John R. Taylor, specifically involving differential calculus and the Chain Rule for Partial Derivatives. The user seeks clarification on an equation where y and η are functions of x, while α is a constant. They express uncertainty about how to apply the Chain Rule and calculate variations in the expression. Suggestions include revisiting the definition of the derivative and injecting a variation of α to derive the result. The conversation emphasizes the importance of understanding the application of calculus in this context.
darwined
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I have been reading Lagrangian from Classical Mechanics by John R. Taylor.
I have adoubt in a derivation which invloves differential calculus.

I have attached snapshot of the equation , can someone please explain.
Here y,η are functions of x but α is s acosntant.

Please let me know if I am not clear.
 

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This is a simple application of the Chain Rule for Partial Derivatives.

If you have a little bit of time, you could derive it by going back to the definition of the derivative.
You would simply inject a variation of α and calculate the variation of the expression.
 
Not sure how to go about it , can you please explain.
 
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