View of /trunk/NationalProblemLibrary/ma122DB/set5/s3_5_17.pg

    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('17')
   21 
   22 DOCUMENT();        # This should be the first executable line in the problem.
   23 
   24 loadMacros(
   25 "PGbasicmacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a_numb = random(2,9,1);
   34 $a_sign = random(-1,1,2);
   35 $a      = $a_numb * $a_sign;
   36 
   37 $b_numb = random(2,9,1);
   38 $b_sign = random(0,0,2);
   39 $b      = $b_numb * $b_sign;
   40 
   41 $c_numb = random(2,9,1);
   42 $c_sign = random(-1,1,2);
   43 $c      = $c_numb * $c_sign;
   44 
   45 $d_numb = random(2,9,1);
   46 $d_sign = random(-1,1,2);
   47 $d      = $d_numb * $d_sign;
   48 
   49 $e_numb = random(2,9,1);
   50 $e_sign = random(-1,1,2);
   51 $e      = $e_numb * $e_sign;
   52 
   53 $m = random(3,8,1);
   54 $n = random(9,15,1);
   55 
   56 BEGIN_TEXT
   57 Let \[ f(x) = ($a x^2 + $c)^{$m} ($d x^2 + $e)^{$n}  \]
   58 $BR
   59 \( f'( x ) = \) \{ans_rule(80) \}
   60 $BR
   61 END_TEXT
   62 
   63 $coeff_1 = 2*$a*$d*($m + $n);
   64 $coeff_2 = $b*$d*($m + 2*$n);
   65 $coeff_3 = 2*($a*$e*$m + $c*$d*$n);
   66 $coeff_4 = $b*$d;
   67 
   68 $exp_1 = $m - 1;
   69 $exp_2 = $n - 1;
   70 
   71 $ans = "($a*x^2+$c)^$exp_1 * ($d*x^2+$e)^$exp_2 * ($coeff_1*x^3 + $coeff_3*x)";
   72 ANS(fun_cmp($ans));
   73 
   74 ENDDOCUMENT();        # This should be the last executable line in the problem.