Total Derivative of a Max Function: Maximizing Social Welfare Function

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?

• Hint: $\mathrm df(x,y,z)=f_x(x,y,z)\mathrm dx+f_y(x,y,z)\mathrm dy+f_z(x,y,z)\mathrm dz$. The first bracket results from the first two summands. – Herr K. Jan 6 at 17:12