Solving Lagrangian Derivation - Classical Mechanics by John R. Taylor

[darwined]

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.

 

[maajdl]

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.

 

[darwined]

Not sure how to go about it , can you please explain.