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

Wed Jun 27 19:34:12 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1041 byte(s)
Updated/Corrected tags.  --JJH


    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
24 "PG.pl",
25 "PGbasicmacros.pl",
26 "PGchoicemacros.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();