Partial/total derivative problem

[Patrick414159]

I have a Euler-Lagrange related problem. Specifically, my text book skips a few steps that I cannot bridge without some help. The problem is this:
Given a function f(y(x), y'(x)), the Euler-Lagrange equation reduces (in differential form) to:

No problem, I can show this. My book then says:
"Since f does not explicitly depend on "x",


I apologize for the weird d/dx on the left, it is a total derivative wrt x. Mathematica insists on formatting it that way for some reason. Anyway, I cannot show that the lhs = the rhs in the second equation, despite many pages of trying which I will omit here. Can anyone show how the second equation is justified step-by-step?

Thanks in advance.

Patrick

 

[Steven G]

You made a mistake by choosing not to show any of the work you have done so far. You you had read the posting guidelines you would have read that we requires posters to show their work as we do not solve problems for students on this website. So please follow the posting guidelines by showing us your work. This way we know which method you want to use and we can see where you are making any mistakes.

 

[Patrick414159]

I am not a student, I do this for fun. If you want to see my work so far here it is (1-3 of 8). I do not think it will be useful as it simply evaluates d/dx of f and of y'fy' and attempts to reconstruct the rhs as indicated in my original post:

You made a mistake by choosing not to show any of the work you have done so far. You you had read the posting guidelines you would have read that we requires posters to show their work as we do not solve problems for students on this website. So please follow the posting guidelines by showing us your work. This way we know which method you want to use and we can see where you are making any mistakes.

 

[Patrick414159]

Here are (4-8 of 8).

 

[Dr.Peterson]

I have a Euler-Lagrange related problem. Specifically, my text book skips a few steps that I cannot bridge without some help. The problem is this:
Given a function f(y(x), y'(x)), the Euler-Lagrange equation reduces (in differential form) to:
View attachment 24105
No problem, I can show this. My book then says:
"Since f does not explicitly depend on "x",
View attachment 24106

Would it be possible to show us an image of the two lines you gave us, with the context leading up to them (and maybe a little after), so we can be more sure what is being said? I think that might help more than your work.