Question: Euler-Lagrange equation

I'm taking a calculus of variations class and checking some answers with Maples VariationalCalculus package and the EulerLagrange command in particular.

I've done an exercise by hand for which I don't get the same results from Maple and I'm trying to see why.

Can anyone help me construct the EL equation "manually", in partcular how do I get the partial derivartive of an expression containing x, y(x) and diff(y(x),x) with respect to diff(y(x),x) ? That is, I want the partial derivative wrt to y' of F(x,y,y') where y is a function of x and y' is dy/dx



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