View of /trunk/NationalProblemLibrary/Rochester/setVmultivariable3ParDer/UR_VC_5_10.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 
    6 ## KEYWORDS('Multivariable','derivative' 'partial')
    7 ## Tagged by tda2d
    8 
    9 ## DBsubject('Calculus')
   10 ## DBchapter('Partial Derivatives')
   11 ## DBsection('Partial Derivatives')
   12 ## Date('')
   13 ## Author('')
   14 ## Institution('Rochester')
   15 ## TitleText1('')
   16 ## EditionText1('')
   17 ## AuthorText1('')
   18 ## Section1('')
   19 ## Problem1('')
   20 
   21 DOCUMENT();
   22 
   23 loadMacros(
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 $a = random(1, 4);
   35 $b = random(1, 4);
   36 $c = random(1, 4);
   37 $d = random(1, 4);
   38 
   39 $dfdx = 2*$a*$b*$d/($a*$c + $b*$d)**2;
   40 $dfdy = -2*$a*$b*$c/($a*$c + $b*$d)**2;
   41 
   42 BEGIN_TEXT
   43 $PAR
   44 Find the first partial derivatives of \( f(x,y) = \frac{${a}x - ${b}y}{${a}x +
   45 ${b}y} \) at the point (x,y) = ($c, $d).
   46 $PAR
   47 \( \frac{\partial f}{\partial x}($c, $d) = \) \{ ans_rule(40) \}
   48 $PAR
   49 \( \frac{\partial f}{\partial y}($c, $d) = \) \{ ans_rule(40) \}
   50 END_TEXT
   51 ANS(num_cmp($dfdx));
   52 ANS(num_cmp($dfdy));
   53 
   54 ENDDOCUMENT();