How do I define implicit functions to be differentiated with the symbolic toolbox?

Im trying to define an implicit function x(t) in the symbolic toolbox which I then want to be able to differentiate with its own time derivative. E.g I want to be able to express a function which has x(t) as its variable and then be able to calculate d/dt(funk), d/dx(funk) and d/dx'(funk).

I have tried:

syms t

x=sym('x(t)');

funk=2*x;

funk_dt=diff(funk,t);

But this wont work when differentiating "funk" with respect to x since x is a function.

So instead I tried:

syms x t

X=sym('X(x,t)');    %X is a function of itself and of t

funk=2*X;

funk_dt=diff(funk,t);

funk_dx=diff(funk,x);

But when I try to take the derivative of "funk" with respect to d/dt(x), e.g.

funk_dxdt=diff(funk,diff(X,t))

this wont work since X is a function, not a variable.

If it helps with interpreting my question, what I want to do is calculate Lagrange's equations. Here I need to calculate:

d/dt(d(L)/d(q')) - d(L)/d(q)

where L is a function of q(t) and q' is the time derivative of q(t).

Grateful for any help!

/Erik