This [answer](https://matheducators.stackexchange.com/a/10584/590), to a question on teaching the chain rule, suggests writing something like this
$$
\frac{\mathrm{d}\, \mathrm{e}^\sqrt{s}}{\mathrm{d}\,s}=\frac{\mathrm{d} \,\mathrm{e}^\sqrt{s}}{\mathrm{d}\sqrt{s}}\frac{\mathrm{d}\sqrt{s}}{\mathrm{d}\,s}
$$
where a composite term ($\sqrt{s}$) is substituted for the variable occurring in the denominator of a derivative $\frac{\mathrm{d}y}{\mathrm{d}x}$. 

It is still common today to substitute a term for $y$ in $\frac{\mathrm{d}y}{\mathrm{d}x}$, but I have rarely (or never) seen people substitute for $x$ in $\frac{\mathrm{d}y}{\mathrm{d}x}$. On the other hand it makes a lot of sense, when the "differential coefficient" $\frac{\mathrm{d}y}{\mathrm{d}x}$ is literally understood as "the coefficient in front of the differential $\mathrm{d}x$ in $\mathrm{d}y=c\mathrm{d}x$".

> Question: Can one find expressions like $\frac{\mathrm{d} \,\mathrm{e}^\sqrt{s}}{\mathrm{d}\sqrt{s}}$ in classical works of differential calculus? Was it popular at some time?