I'm studying public economics but my question here is purely mathematical in nature. I have a function:
$$ V(1-\tau, R) = \max_zu((1-\tau)z+R,z) $$
I need to take the total derivative of this, in my notes, I'm told it is equal to
$$ dV=u_c [-zd\tau + dR] + dz[(1-\tau)u_c + u_z] $$
where $c^i=(1-\tau)z^i+R$, $\tau$ is the tax rate, R is government revenue, z is income, V is the indirect utility function.
and the notation $u_c$ denotes the derivative of u with respect to c.
Is the first bracket the partial derivative with respect to c and the second the partial derivative with respect to z?