# PartialDerivative

Makes an object a partial derivative.

Makes an object a partial derivative, i.e. a derivative which
commutes. The object on which it acts has to be a non-sub/superscript
child, while all the sub- or superscript child nodes are interpreted
to be the variables with respect to which the derivative is taken.\partial{#}::PartialDerivative.
A_{\mu}::Depends(\partial).
ex:= \partial_{\nu}{A_{\mu} B_{\rho}};

\(\displaystyle{}\partial_{\nu}(A_{\mu} B_{\rho})\)

product_rule(_);

\(\displaystyle{}\partial_{\nu}(A_{\mu}) B_{\rho}+A_{\mu} \partial_{\nu}(B_{\rho})\)

unwrap(_);

\(\displaystyle{}\partial_{\nu}(A_{\mu}) B_{\rho}\)

Note that derivative objects do not necessarily need to have a sub- or
superscript child, they can be abstract derivatives as in

D{#}::PartialDerivative.
ex:= D(c d e);

\(\displaystyle{}D(c d e)\)

product_rule(_);

\(\displaystyle{}D(c) d e+c D(d) e+c d D(e)\)

If you want to write a derivative with respect to a coordinate (instead
of with respect to an index, as in the first example above), refer to
the

`Coordinate`

property.