You can't calculate the "total differential" of an EQUATION.
The total differential of a function f(z,y,x,w,v...) is defined as
(df/dz) dz + (df/dy) dy + (df/dx) dx + (df/dw) dw + (df/dv) dv ...
where all of the derivatives are "partials."
An example may help:
f(p,q,r,s) = pq cos(q) - p/(r+s).
The total differential of f is
[q*cos(q) - 1/(r+s)] dp + [p*cos(q) - pq*sin(q)] dq + [p/(r+s)^2] dr + [p/(r+s)^2] ds.