How to find D[F[a(x,y,t),b(x,y,t)], t]in terms of D[F[a(x,y,t),b(x,y,t)]X]and D[F[a(x,y,t),b(x,y,t)], y]?

I have a function $ F (a (x, y, t), b (x, y, t)) $ which I would like to display the derivative

$ frac { partial F} { partial t} = f (x, y, t) frac { partial F} { partial x} + g (x, y, t) frac { partial F} { partial y}
$

now, I'm only doing

$ frac { partial F} { partial t} = f (x, y, t) frac { partial F} { partial a} + g (x, y, t) frac { partial F} { partial b}
$

trying $ frac { partial F} { partial a} = frac { partial F} { partial x} frac { partial x} { partial a} $ gives me the error that $ a (x, y, t) $ is not a valid variable.

P.S .: here I use $ a (x, y) $ as a placeholder, the actual error message is as follows:

General :: ivar: x Cos

because in my problem $ a (x, y, t) = x cos t + y sin t $

Is my approach to $ frac { partial F} { partial a} = frac { partial F} { partial x} frac { partial x} { partial a} $ is wrong? Any idea appreciated.