The esdiff
package has handy macros for derivatives and partial derivatives, taking care of indices.
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathtools}
\usepackage[thinc]{esdiff}
\begin{document}
First order derivative: df/dx
\begin{equation}
\diff{f}{x}
\end{equation}
Fourth order derivative: d4f/dx4|x=1
\begin{equation}
\diff*[4]{f}{x}{x = 1}
\end{equation}
First order partial derivative:
\begin{equation}
\diffp{f}{x}
\end{equation}
Second order crossed partial derivative
\begin{equation}
\diffp{g}{tu}
\end{equation}
\end{document}