= Solution
Assume that the optical continuum is dominated by <Rayleigh scattering> by particles much smaller than the wavelength, and that their column abundance is fixed. Their cross-section, hence the slant <optical depth>, scales as $\tau_\lambda\propto\lambda^{-4}$. Differentiating the <annulus model for transmission spectroscopy> exactly gives the <logarithmic slope of total transit depth>
$$
\boxed{\frac{d\ln\delta_\lambda}{d\ln\lambda}
=-4\frac{B\tau_\lambda e^{-\tau_\lambda}}{A+B(1-e^{-\tau_\lambda})}}.
$$
For $A\geq0$ and $B>0$, the slope lies between $-4$ and zero, but generally depends on wavelength. In the <optically thin> limit, $\delta_\lambda\simeq A+B\tau_\lambda$, so its slope is $-4B\tau_\lambda/(A+B\tau_\lambda)$. It vanishes as the atmospheric signal becomes negligible compared with the opaque disc; it also approaches zero in the saturated <optically thick> limit.
The familiar value $m\simeq-4$ applies to the <optically thin> atmospheric excess,
$$
\boxed{\frac{d\ln(\delta_\lambda-A)}{d\ln\lambda}\simeq-4},
$$
or formally to a model in which $A$ is negligible. For an ordinary thin <exoplanet atmosphere>, however, $B/A\simeq2H/R_p\ll1$, so neglecting the opaque planetary baseline in the total transit depth is not usually justified. \b[A universal $m=-4$ for the logarithm of the total transit depth does not follow from the stated model.]
In a stratified <isothermal atmosphere>, the related <scattering slope of a transmission spectrum> is instead $dR_{\rm tr}/d\ln\lambda=-4h$, obtained by moving the effective tangent level to keep its slant <optical depth> of order unity. Consequently $d\ln\delta/d\ln\lambda=-8h/R_{\rm tr}$ there. The radius slope, atmospheric-excess slope and total-depth slope are different observables.
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