= Solution
Hold liquid-water content and <cloud> thickness fixed, as required for a partial sensitivity to droplet number. Then $\tau=K N_d^{1/3}$, so $d\tau/dN_d=\tau/(3N_d)$. Differentiating the <albedo> relation gives $dA/d\tau=7/(\tau+7)^2$, hence
$$
\frac{dA}{dN_d}=\frac{7\tau}{3N_d(\tau+7)^2}.
$$
Since $A=\tau/(\tau+7)$ and $1-A=7/(\tau+7)$,
$$
\boxed{\frac{dA}{dN_d}=\frac{A(1-A)}{3N_d}.}
$$
The factor $A(1-A)$ peaks at $A=1/2$, so the <albedo> response to a fixed fractional droplet-number change is greatest at intermediate <albedo> and weaker near either saturation limit.
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