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```Update to current Union versions (using MathObjects)
```

```    1 ## DESCRIPTION
2 ##   Calculate Gradient and Directional Derivative
3 ## ENDDESCRIPTION
4
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Partial Derivatives')
10 ## DBsection('Directional Derivatives and the Gradient Vector')
11 ## Date('8/23/07')
12 ## Author('')
13 ## Institution('Union College')
14 ## TitleText1('Calculus')
15 ## EditionText1('7')
16 ## AuthorText1('Anton')
17 ## Section1('14.6')
18 ## Problem1('1')
19 ## TitleText2('Calculus: Early Transcendentals')
20 ## EditionText2('1')
21 ## AuthorText2('Rogawski')
22 ## Section2('14.5')
23 ## Problem2('21 22 23 24 25 26 27 28 29 30')
24
25 DOCUMENT();        # This should be the first executable line in the problem.
26
28   "PGstandard.pl",
29   "PGunion.pl",
30   "MathObjects.pl",
31   "parserVectorUtils.pl",
32   "PGcourse.pl",
33 );
34
35
36 TEXT(beginproblem);
37
38 ##############################################
39 #  Setup
40
41 Context("Vector")->flags->set(
42   reduceConstants => 0,
43   reduceConstantFunctions => 0,
44 );
45
46 #
47 #  The function
48 #
49 \$a = random(1,5,1);
50 \$b = random(2,5,1);
51
52 \$f = Formula("(\$a + \$b x y)^(3/2)");
53
54 #
55 #  The point
56 #
57 (\$x,\$y) = (random(1,5,1),random(1,5,1));
58
59 #
60 #  The unit vector
61 #
62 \$u = non_zero_vector2D(-2,2);
63 \$d = (\$u.\$u); \$U = \$u->TeX."/".Formula("sqrt(\$d)")->TeX;
64
65 #
66 #  The derivatives
67 #
68 \$fx = \$f->D('x');
69 \$fy = \$f->D('y');
70
72 \$Duf = \$gradf->eval(x=>\$x,y=>\$y) . unit(\$u);
73
74 ##############################################
75 #  Main text
76
77 \$uu = BoldMath('u');
78
79 Context()->texStrings;
80 BEGIN_TEXT
81
82 Let \(f(x,y) = \$f\).
83 Then \(\$GRAD\!f\) = \{ans_rule(50)\}, and \(D_{\$uu} f(\$x,\$y)\) for
84 \(\$uu = \$U\) is \{ans_rule(30)\}.
85
86 END_TEXT
87 Context()->normalStrings;
88
89 ##################################################
91
92 ANS(