Math::Symbolic::Derivative - Derive Math::Symbolic trees

       Please send feedback, bug reports, and support requests to the Math::Symbolic support mailing list: math-
       symbolic-support at lists dot sourceforge dot net. Please consider letting us know how you use
       Math::Symbolic. Thank you.

       If you're interested in helping with the development or extending the module's functionality, please
       contact the developers' mailing list: math-symbolic-develop at lists dot sourceforge dot net.

       List of contributors:

         Steffen M�ller, symbolic-module at steffen-mueller dot net
         Stray Toaster, mwk at users dot sourceforge dot net
         Oliver Ebenh�h

       The package variable %Partial_Rules contains partial derivative rules as key-value pairs of names and
       subroutines.

       This module implements derivatives for Math::Symbolic trees.  Derivatives are Math::Symbolic::Operators,
       but their implementation is drawn from this module because it is significantly more complex than the
       implementation of most operators.

       Derivatives come in two flavours. There are partial- and total derivatives.

       Explaining the precise difference between partial- and total derivatives is beyond the scope of this
       document, but in the context of Math::Symbolic, the difference is simply that partial derivatives just
       derive in terms of explicit dependency on the differential variable while total derivatives recongnize
       implicit dependencies from variable signatures.

       Partial derivatives are faster, have been tested more thoroughly, and are probably what you want for
       simpler applications anyway.

   EXPORT
       None by default. But you may choose to import the total_derivative() and partial_derivative() functions.

       Math::Symbolic::Derivative - Derive Math::Symbolic trees

       New versions of this module can be found on http://steffen-mueller.net or CPAN. The module development
       takes place on Sourceforge at http://sourceforge.net/projects/math-symbolic/

       Math::Symbolic

perl v5.40.0                                       2024-09-16                    Math::Symbolic::Derivative(3pm)

partial_derivative
       Takes a Math::Symbolic tree and a Math::Symbolic::Variable as argument.  third argument is an optional
       boolean indicating whether or not the tree has to be cloned before being derived. If it is true, the
       subroutine happily stomps on any code that might rely on any components of the Math::Symbolic tree that
       was passed to the sub as first argument.

   total_derivative
       Takes a Math::Symbolic tree and a Math::Symbolic::Variable as argument.  third argument is an optional
       boolean indicating whether or not the tree has to be cloned before being derived. If it is true, the
       subroutine happily stomps on any code that might rely on any components of the Math::Symbolic tree that
       was passed to the sub as first argument.

         use Math::Symbolic::Derivative qw/:all/;
         $derived = partial_derivative($term, $variable);
         # or:
         $derived = total_derivative($term, $variable);