I'm slowly working my way through this sheet, but I keep encountering things not in the notes. I'm also having trouble understanding what wikipedia has to say: Euler?Lagrange equation - Wikipedia, the free encyclopediaQuote:

Write down the Euler-Lagrane equations for critical points of the functional I of two functions where:

I have a function so my first equation is:

The second equation would be the same but with instead of .

Am I reading this correctly?