= Cloud albedo susceptibility
{title2=$dA/dN_d=A(1-A)/(3N_d)$}
For $\tau\propto N_d^{1/3}$ at fixed liquid-water content and thickness, and $A=\tau/(\tau+7)$, the derivative is $dA/dN_d=A(1-A)/(3N_d)$. For a fixed fractional number increase, the initial response is greatest at $A=1/2$. The exact finite-change expression is $A'=sA/(1-A+sA)$ with $s=(N_d'/N_d)^{1/3}$. Uncertain activation of additional particles and changes in <water> content limit direct application to real <clouds>.
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