View of /trunk/NationalProblemLibrary/ma122DB/set5/s3_5_53.pg

    1 ##  KEYWORDS('derivatives', 'chain rule')
    2 ##DESCRIPTION
    3 ##  using chain rule
    4 ##ENDDESCRIPTION
    5 
    6 ## Shotwell cleaned
    7 ## tcao , PAID on 11-24-2003
    8 
    9 ## DBsubject('Calculus')
   10 ## DBchapter('Differentiation')
   11 ## DBsection('The Chain Rule')
   12 ## Date('6/3/2002')
   13 ## Author('')
   14 ## Institution('')
   15 ## TitleText1('Calculus: Early Transcendentals')
   16 ## EditionText1('6')
   17 ## AuthorText1('Stewart')
   18 ## Section1('3.4')
   19 ## Problem1('53')
   20 
   21 DOCUMENT();
   22 # 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 = random(3,9,1);
   34 $b1 = random(2,15,1);
   35 $b2 = random(2,3,1);
   36 $b4 = random(2,15,1);
   37 $b3 = random(2,15,1);
   38 $a1 = $a-1;
   39 
   40 BEGIN_TEXT
   41 $BR
   42 Let \( F(x)= f(x^{$a}) \) and \( G(x)=(f(x))^{$a} \) and suppose that $BR$BR
   43 \[ a^{$a1}=$b1, \quad f(a)=$b2, \quad f'(a)=$b3, \quad f'(a^{$a})=$b4 \]
   44 $BR
   45 Find \( F'(a) \) and \( G'(a) \). $BR$BR
   46 \(F'(a)=\) \{ans_rule(10) \}  $BR
   47 \(G'(a)=\) \{ans_rule(10) \}
   48 
   49 END_TEXT
   50 
   51 $ans1 = "$a*$b1*$b4";
   52 $ans2 = "$a*($b2^$a1)*$b3";
   53 ANS(num_cmp($ans1));
   54 ANS(num_cmp($ans2));
   55 
   56 ENDDOCUMENT();
   57 # This should be the last executable line in the problem.
   58