[npl] / trunk / NationalProblemLibrary / ma122DB / set5 / s3_5_17.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Wed Jul 18 00:35:17 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1606 byte(s)
```Changed Stew4e to Stew 6e.
```

```    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
25 "PGbasicmacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
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.
```