View of /trunk/NationalProblemLibrary/Union/setDervChainRule/an3_5_27.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('derivative' 'chain rule')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differentiation')
   10 ## DBsection('The Chain Rule')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Union College')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23   "PG.pl",
   24   "PGbasicmacros.pl",
   25   "PGchoicemacros.pl",
   26   "PGanswermacros.pl",
   27   "PGauxiliaryFunctions.pl",
   28   "PGunion.pl",        # Union College utilities
   29   "PGcourse.pl",       # Customization file for the course
   30 );
   31 
   32 TEXT(beginproblem());
   33 BEGIN_PROBLEM();
   34 
   35 $a = non_zero_random(-4,4,1);
   36 $b = non_zero_random(-5,5,1);
   37 $expa = $a-1;
   38 
   39 $df = "[${a}x^($expa)]sec($b/x)+x^($a)*[sec($b/x)tan($b/x)*(-$b/x^2)]";
   40 
   41 BEGIN_TEXT
   42 Suppose that \( f(x) = x^{$a}\sec\left( \displaystyle \frac{$b}{x} \right) \).
   43 Find \(f'(x)\).
   44 $PAR
   45 \(f'(x)\) = \{ans_rule(60)\}.
   46 END_TEXT
   47 
   48 $showPartialCorrectAnswers=1;
   49 
   50 ANS(fun_cmp(
   51   $df,                   #  the correct answer
   52   limits => [.1,1],       #  range of x's to use
   53   relTol => .1,          # .1 percent, (i.e., .001)
   54 ));
   55 
   56 ##################################################
   57 
   58 END_PROBLEM();
   59 ENDDOCUMENT();        # This should be the last executable line in the problem.