Question: help defining and differentiating a function

Hi guys, 

I need help with differentiating a function I have defined. Here is the function I have:

The right hand side of this expression is a solution I have previously found via Maple, I know that this is correct. Basically I have a function a that is dependent on the another functon u(x,y,t).

Now the way I have defined this gives me the RHS of the above equation which is what I want. However, what I now need to do is to show that this constant function _F1(x,y,t) is equal to zero. I know this to be true via hand calcuations, but to do so I need to sub it into another equation where it has the derivatives of a. The way the derivatives are defined is through the D function. But this doesn't seem to work with how I have defined the function previously.

D[1](a)(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t)) 

This should give me 

-4*diff(u(x,y,t),x,x,x)+diff(_F1(x,y,t),x)
However it just repeats what I input. I have tried defining the function in a different way,

a:=(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t)) ->-4*diff(u(x,y,t),x,x)+_F1(x,y,t)

However this returns an error where I am not allowed to define this.

Can anyone help, would be a massive help. Thanks in advance.