###########################################################
#
#  Example showing how to use the Parser's differentiation
#  capabilities.
#

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGbasicmacros.pl",
  "PGanswermacros.pl",
  "Parser.pl",
  "Differentiation.pl",
);

TEXT(beginproblem());

###########################################################
#
#   Use standard numeric mode
#
Context('Numeric');
$x = Formula('x');  # used to construct formulas below.

#
#   Define a function and its derivative and make them pretty
#
$a = random(1,8,1);
$b = random(-8,8,1);
$c = random(-8,8,1);

$f = ($a*$x**2 + $b*$x + $c) -> reduce;
$df = $f->D('x');

$x = random(-8,8,1);

###########################################################
#
#  The problem text
#
BEGIN_TEXT

Suppose \(f(x) = \{$f->TeX\}\).
$PAR
Then \(f'(x)=\) \{ans_rule(20)\},$BR
and \(f'($x)=\) \{ans_rule(20)\}.
$PAR
(Same as previous problem, but using the formal differentiation package.
Note that automatic differentiation does not always produce the simples form.)

END_TEXT

###########################################################
#
#  The answers
#
ANS(fun_cmp($df->string));
ANS(num_cmp($df->eval(x=>$x)));
$showPartialCorrectAnswers = 1;

###########################################################

ENDDOCUMENT();        # This should be the last executable line in the problem.