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

 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.