Derivative of a time derivative function

Hi, I have the following code:

syms w(t) u(t)

a=atan(w/u)
a_dot=diff(a,t)

Up to this point is everything ok, but now I need to derivate a_dot respect to u:

a_dot_u=diff(a_dot,u)

The last line runs the following error message: "All arguments, except for the first one, must not be symbolic functions".

¿How can I fix it?