The differential command computes the differential of an algebraic expression, and returns a OneForm object

The differential of a function f on a space with coordinates $\left(x_1\,x_2\,\dots \,x_n\right)$ is $\mathrm{df}\=\sum _{i\=1}^n$ $\frac{\partial }{\partial x_i}f\left(x_1\,\mathrm{..}\,x_n\right)$ $\cdot {\mathrm{dx}}_i$. See differential.

The space on which f lives can be specified using the space= option. It may be necessary to specify this option if the expression f contains names that are not coordinates, or if f is independent of a name that is a coordinate.

The Differential command maps itself over indexed structures such as lists and vectors.

This command is part of the LieAlgebrasOfVectorFields package. It can be called using the form Differential(...) after executing the command with(LieAlgebrasOfVectorFields). It can also be directly called using the form :-LieAlgebrasOfVectorFields[Differential](...). The Differential command returns a OneForm object.  For more detail see Overview of the OneForm object.

$\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right)\:$

$\mathrm{Differential}\left(f\left(x\,y\right)\right)$

$\left(\frac{\partial }{\partial x}f\left(x\,y\right)\right)\mathrm{dx}+\left(\frac{\partial }{\partial y}f\left(x\,y\right)\right)\mathrm{dy}$

$\mathrm{Differential}\left(a^2{y}^2\,\mathrm{space}=\left[x\,y\right]\right)$

$2a^{2}y\mathrm{dy}$

$\mathrm{Differential}\left(\left[x^2\,y^2\,2xy\right]\,\mathrm{space}=\left[x\,y\right]\right)$

$\left[2x\mathrm{dx}\,2y\mathrm{dy}\,2y\mathrm{dx}+2x\mathrm{dy}\right]$

The LieAlgebrasOfVectorFields[Differential] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.