There are several equivalent mathematical notations used to represent the partial derivative of a multivariate function $y = f(x_1, x_2, \ldots, x_n)$ with respect to its $i^{ extrm{th}}$ parameter, $x_i$. Common conventions include fractional forms like $\frac{\partial y}{\partial x_i}$ and $\frac{\partial f}{\partial x_i}$, subscripted differential operators such as $\partial_{x_i} f$, $\partial_i f$, $D_i f$, and $D_{x_i} f$, as well as subscripted function names like $f_{x_i}$ and $f_i$.