How would you tackle the following Lagrangian derivative?

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Mike Meyers
Mike Meyers 2018-1-19
Imagine you are modeling a system, and have obtained a Lagrangian equation which includes a time derivative of a variable.
How would you obtain a partial derivative with respect to that variable, as it seems that Matlab cannot use diff or functionalDerivative with a time function (for example, x(t)) as a parameter?
equation in question:
L(t) = (3*theta2(t))/4 - (3*theta1(t))/4 + (69468677223508225*x(t))/9007199254740992 + diff(theta1(t), t)^2/5000 +
diff(theta2(t), t)^2/5000 + (7*diff(x(t), t)^2)/40 - 100*x(t)^2 - 25*((3*theta1(t))/100 - (3*theta2(t))/100)^2
How would you derive this with respect to theta1(t), theta2(t), and x(t)?
So far, I have tried:
Eq1 = diff(functionalDerivative(L, diff(theta1(t),t),t);
Eq1 = functionalDerivative(functionalDerivative(L, diff(theta1(t),t)))
etc.
Any ideas? Can it even be done?

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