How to master $\LaTeX$ in physics

This is a brief summary of Do’s and Don’ts when writing equations with $\LaTeX$ in physics.
In advance: use the $\LaTeX$-packages

Using those packages as a guide prevents about 90% of all common $\LaTeX$-NoGoes. Have a look at their documentation!

	Good	Bad	Explanation
Total derivative	`\dv{f}{x}`: $\displaystyle\frac{\operatorname{d}\!f}{\operatorname{d}\!x}$	`\frac{df}{dx}`: $\displaystyle \frac{df}{dx}$	The “differential”-$\mathrm{d}$ should always be non-italic.
Total derivative (higher order)	`\dv[n]{f}{x}`: $\displaystyle\frac{\operatorname{d}^{n}\!f}{\operatorname{d}\!x^{n}}$	`\frac{d^{n}f}{dx^{n}}`: $\displaystyle \frac{d^{n}f}{dx^{n}}$
Partial derivative
Partial derivative (higher order)
$1$-dimensional Integral	`\int\limits_{x_{1}}^{x_{2}} \dd{x} f(x)` : $\displaystyle \int\limits_{x_{1}}^{x_{2}}\!\!\operatorname{d}\!x\, f(x)$	`\int_{x_{1}}^{x_{2}} dx f(x)` : $\displaystyle \int_{x_{1}}^{x_{2}} dx f(x)$
$n$-dimensional Integral	`\int\limits_{\R^{n}} \dd[n]{x} f(x)`: $\displaystyle \int\limits_{\mathbb{R}^{n}}\!\!\operatorname{d}^{n}\!x\, f(x)$
Surface integral over a vector field	$\displaystyle \int\limits_{S}\!\!\operatorname{d}\!S\, \hat{\boldsymbol{n}}_{\perp S} \boldsymbol{\cdot} \boldsymbol{E}(\boldsymbol{r})$
Reserved mathematical letters (i.e.: Euler’s number $\mathrm{e}$, imaginary unit $\mathrm{i}$, …)	`\mathrm{e}^{\mathrm{i}x} = \cos(x) + \mathrm{i} \sin(x)` : $\mathrm{e}^{\mathrm{i}x} = \cos(x) + \mathrm{i} \sin(x)$	`e^{ix} = cos(x) + i sin(x)` : $e^{ix} = cos(x) + i sin(x)$

	Good	Bad	Explanation
Total derivative	`\dv{f}{x}`: \(\displaystyle\frac{\operatorname{d}\!f}{\operatorname{d}\!x}\)	`\frac{df}{dx}`: \(\displaystyle \frac{df}{dx}\)	The “differential”-$\mathrm{d}$ should always be non-italic.
Total derivative (higher order)	`\dv[n]{f}{x}`: \(\displaystyle\frac{\operatorname{d}^{n}\!f}{\operatorname{d}\!x^{n}}\)	`\frac{d^{n}f}{dx^{n}}`: \(\displaystyle \frac{d^{n}f}{dx^{n}}\)
Partial derivative
Partial derivative (higher order)
$1$-dimensional Integral	`\int\limits_{x_{1}}^{x_{2}} \dd{x} f(x)` : \(\displaystyle \int\limits_{x_{1}}^{x_{2}}\!\!\operatorname{d}\!x\, f(x)\)	`\int_{x_{1}}^{x_{2}} dx f(x)` : \(\displaystyle \int_{x_{1}}^{x_{2}} dx f(x)\)
$n$-dimensional Integral	`\int\limits_{\R^{n}} \dd[n]{x} f(x)`: \(\displaystyle \int\limits_{\mathbb{R}^{n}}\!\!\operatorname{d}^{n}\!x\, f(x)\)
Surface integral over a vector field	\(\displaystyle \int\limits_{S}\!\!\operatorname{d}\!S\, \hat{\boldsymbol{n}}_{\perp S} \boldsymbol{\cdot} \boldsymbol{E}(\boldsymbol{r})\)
Reserved mathematical letters (i.e.: Euler’s number $\mathrm{e}$, imaginary unit $\mathrm{i}$, …)	`\mathrm{e}^{\mathrm{i}x} = \cos(x) + \mathrm{i} \sin(x)` : \(\mathrm{e}^{\mathrm{i}x} = \cos(x) + \mathrm{i} \sin(x)\)	`e^{ix} = cos(x) + i sin(x)` : \(e^{ix} = cos(x) + i sin(x)\)