This is not a homework question but one that is part of the course material and I can't really move on until I understand the basic calculus.(adsbygoogle = window.adsbygoogle || []).push({});

I have a problem interpreting "d by dx of partial dF by dy' equals partial d by dy' of dF by dx" in the following question, which I set out and then highlight my problem.

For F = (x^2 + y'^2)^1/2, find;

partial dF/dx = x(x^2 + y'^2)^-1/2

partial dF/dy = 0

partial dF/dy' = y'(x^2 + y'^2)^-1/2

dF/dx = p.dF/dx + p.dF/dy.y' + p.dF/dy'.y''

Show that: d/dx(p.dF/dy') = p.d/dy'(dF/dx)

Taking the RHS I believe is:

p.d/dy'(dF/dx) = p.d/dy'[x(x^2 + y'^2)^-1/2 + p.dF/dy.y' +

y'(x^2 + y'^2)^-1/2 y'']

ditto = - xy'(x^2 + y'^2)^3/2 + p.d/dy' pdF/dy.y'

- y'^2 y''(x^2 + y'^2)^3/2

My problem is that I have forgotten how to interprete p.d/dy' pdF/dy.y' I know that the answer is y''(x^2 + y'^2)^-1/2 but I don't understand how one gets this answer when partial dF/dy = 0

and I don't know how to interpret the LHS - d/dx(partial dF/dy') at all although I appreciate that it gives the same answer for this function as the RHS.

I would appreciate some help on the fundamentals. Many thanks.

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# Simple calculus - interpretation Euler-Lagrange equation

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