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

Thu Aug 17 17:23:36 2006 UTC (6 years, 10 months ago) by jjholt
File size: 1335 byte(s)
Added tags.


    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
23   "PG.pl",
24   "PGbasicmacros.pl",
25   "PGchoicemacros.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.