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lines 9-42 of file: example/general/change_param.cpp
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{xrst_begin change_param.cpp}

Computing a Jacobian With Constants that Change
###############################################

Purpose
*******
In this example we use two levels of taping so that a derivative
can have constant parameters that can be changed. To be specific,
we consider the function :math:`f : \B{R}^2 \rightarrow \B{R}^2`

.. math::

   f(x) = p \left( \begin{array}{c}
      \sin( x_0 ) \\
      \sin( x_1 )
   \end{array} \right)

were :math:`p \in \B{R}` is a parameter.
The Jacobian of this function is

.. math::

   g(x,p) = p \left( \begin{array}{cc}
      \cos( x_0 ) & 0 \\
      0           & \cos( x_1 )
   \end{array} \right)

In this example we use two levels of AD to avoid computing
the partial of :math:`f(x)` with respect to :math:`p`,
but still allow for the evaluation of :math:`g(x, p)`
at different values of :math:`p`.

{xrst_end change_param.cpp}