Solving Lagrangian Derivation - Classical Mechanics by John R. Taylor

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The discussion focuses on the application of the Chain Rule for Partial Derivatives in the context of Lagrangian mechanics, specifically referencing John R. Taylor's "Classical Mechanics." A user seeks clarification on a derivation involving functions y and η, which depend on x, while α remains a constant. The solution involves injecting a variation of α and calculating the corresponding variation of the expression, emphasizing the importance of understanding differential calculus in this context.

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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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