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finding the derivative of a functional w.r.t a function

I've defined a system as:

var('a, t'); function('x, y');

de1 = diff(x(t),t) == y(t); de2 = diff(y(t),t) == -ax(t) - (a-4)/ay(t) - y(t)^3;

I'd like to compute the derivatives of the rhs of de1 and de2 w.r.t to x(t) and y(t) (to eventually form a Jacobian matrix), i.e. the derivative of the rhs of de1 w.r.t to x(t) is Zero and w.r.t y(t) is 1. I've tried the following:

diff(de1.rhs(),y); diff(de1.rhs(),y(t)); derivative(de1.rhs(),y(t));

I get errors on all three. I'd appreciate any help. thank you.