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| 1 : | gage | 5 | ##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 : | jj | 16 | ## DBchapter('Differentiation') |
| 12 : | gage | 5 | ## DBsection('The Chain Rule') |
| 13 : | ## Date('6/3/2002') | ||
| 14 : | ## Author('') | ||
| 15 : | ## Institution('') | ||
| 16 : | jjholt | 453 | ## TitleText1('Calculus: Early Transcendentals') |
| 17 : | gage | 5 | ## EditionText1('4') |
| 18 : | ## AuthorText1('Stewart') | ||
| 19 : | ## Section1('3.5') | ||
| 20 : | ## Problem1('38') | ||
| 21 : | |||
| 22 : | |||
| 23 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 24 : | |||
| 25 : | loadMacros( | ||
| 26 : | "PGbasicmacros.pl", | ||
| 27 : | "PGanswermacros.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(30) \} | ||
| 67 : | |||
| 68 : | END_TEXT | ||
| 69 : | ANS(fun_cmp($ans)); | ||
| 70 : | |||
| 71 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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