# 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.