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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Simple calculus - interpretation Euler-Lagrange equation

**Physics Forums | Science Articles, Homework Help, Discussion**