Writing infinitesimal (differential) element in cursive form

Question

I always write dx ,ds dphi dtheta in cursive form and I also wanted to write it in latex .

How can I achieve it?

One of reason(s) that I wanted to do so is that , for instance as we observe ds, then it can be interpreted as d times s however generally ds is a one constant. So I want to remove that ambiguity.

Concretely , I want to connect 2 symbols with a single stroke.

The below left ones are the one-stroked and the right ones are 2-stroked.

I should have written the bottom left ds with more small s .

Answer 1

Pick a script font of your choice, and build it into the macro \differential. I also chose newtxmath because it looked more compatible with the script font.

\documentclass{article}
\usepackage{amsmath,newtxmath}
\usepackage{aurical}
\usepackage[T1]{fontenc}
\newcommand\differential[1]{\mkern2mu\text{{\Fontauri d}$\mkern-1mu#1$}}
\begin{document}
\[
\int_0^1 x^2 \differential{x}
\]
\[
\int_0^{\pi/2} \theta^2 \differential{\theta}
\]
\[
\int_0^1 s^2 \differential{s}
\]
\end{document}

Here is a version with eulervm for the default math font.

\documentclass{article}
\usepackage{amsmath,eulervm}
\usepackage{aurical}
\usepackage[T1]{fontenc}
\newcommand\differential[1]{\mkern2mu\text{{\Fontauri d}$\mkern-1.5mu#1$}}
\begin{document}
\[
\int_0^1 x^2 \differential{x}
\]
\[
\int_0^{\pi/2} \theta^2 \differential{\theta}
\]
\[
\int_0^1 s^2 \differential{s}
\]
\end{document}

Answer 2

As the Latins wrote and they said...

"There's no disputing on the tastes." or like the comment of the very nice user @Steven B. Segletes "there is no accounting for taste." or "To each, his own".

I would to use a calligraphic font taken from mathalfa package, option cal.

\documentclass[a4paper,12pt]{article}
\usepackage[cal=boondox]{mathalfa}
\newcommand\dif[1]{\mathcal{d}{\!#1}}
\newcommand\difs[1]{\mathcal{d}{\!\mathcal#1}}
\begin{document}

\[\int^{n}_{i=1}{a_i\log(x)\dif{x}}\]

\[ax\difs{s}\]
\end{document}

It is possibile to use in math mode also using frcursive package that you can see the documentation here, https://ctan.mirror.garr.it/mirrors/ctan/fonts/frcursive/frcursive.pdf. But with a lot of humilty I not see a good visual solution.