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# View of /trunk/NationalProblemLibrary/ma122DB/set5/s3_5_38a.pg

Tue Nov 27 20:10:07 2007 UTC (5 years, 5 months ago) by jj
File size: 1515 byte(s)
Fixed bug 1394, typo in the answer in one case.


    1 ##KEYWORDS('derivatives', 'chain rule')
2 ##DESCRIPTION
3 ##  Find a derivative of an expression
4 ##  involving trig functions; requires use of chain rule
5 ##ENDDESCRIPTION
6
7 ## Shotwell cleaned
8 ## tcao , PAID on 11-24-2003
9
10 ## DBsubject('Calculus')
11 ## DBchapter('Differentiation')
12 ## DBsection('The Chain Rule')
13 ## Date('6/3/2002')
14 ## Author('')
15 ## Institution('')
16 ## TitleText1('Calculus: Early Transcendentals')
17 ## EditionText1('6')
18 ## AuthorText1('Stewart')
19 ## Section1('3.4')
20 ## Problem1('38')
21
22
23 DOCUMENT();        # This should be the first executable line in the problem.
24
26 "PGbasicmacros.pl",
28 "PGauxiliaryFunctions.pl"
29 );
30
31 TEXT(beginproblem());
32 $showPartialCorrectAnswers = 1; 33 34$a_gen  = random(2,9,1);
35 $a_sign = random(-1,1,2); 36$a      = $a_gen *$a_sign;
37
38 $n = random(2,8,1); 39 40$gen = random(0,3,1);
41
42 if ($gen == 0) { 43$trig1 = "\sin";
44   $trig2 = "\sin"; 45$ans  = "$a*$n*x^($n-1)*cos(sin(x^($n)))*cos(x^($n))"; 46 } 47 if ($gen == 1) {
48   $trig1 = "\sin"; 49$trig2 = "\cos";
50   $ans = "-$a*$n*x^($n-1)*cos(cos(x^($n)))*sin(x^($n))";
51   }
52 if ($gen == 2) { 53$trig1 = "\cos";
54   $trig2 = "\sin"; 55$ans  = "-$a*$n*x^($n-1)*sin(sin(x^($n)))*cos(x^($n))"; 56 } 57 if ($gen == 3) {
58   $trig1 = "\cos"; 59$trig2 = "\cos";
60   $ans = "$a*$n*x^($n-1)*sin(cos(x^($n)))*sin(x^($n))";
61   }
62
63 BEGIN_TEXT
64 Let $$f(x) = a trig1 ( trig2 ( x ^{n} ))$$. $BR$BR
65
66 $$f'( x ) =$$ \{ans_rule(50) \}
67 END_TEXT
68 ANS(fun_cmp(\$ans));
69
70 ENDDOCUMENT();        # This should be the last executable line in the problem.