##DESCRIPTION ##KEYWORDS('derivatives', 'trigonometry', 'product rule') ## Find a derivative of a function involving trigonometric functions, ## and evalute it at a given point; requires using product rule ##ENDDESCRIPTION DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); \$showPartialCorrectAnswers = 1; \$pi = arccos(-1); \$a_n = random(2,12,1); \$a_s = random(-1,1,2); \$a = \$a_n * \$a_s; \$x_d = random(3,6,1); while (\$x_d == 5) {\$x_d = random(3,6,1);}; \$q = random(0,1,1); if (\$q == 0) { \$x_n = 1; \$x_s = -1; \$x_sign = '-'; }; if (\$q == 1) { \$x_n = 1; \$x_s = 1; \$x_sign = ''; }; if (\$q == 2) { \$x_n = \$x_d - 1; \$x_s = 1; \$x_sign = ''; }; if (\$q == 3) { \$x_n = \$x_d + 1; \$x_s = 1; \$x_sign = ''; }; if (\$q == 4) { \$x_n = 2 * \$x_d - 1; \$x_s = 1; \$x_sign = ''; }; if (\$x_n != 1) { \$x_num = \$x_n }; if (\$x_n == 1) { \$x_num = '' }; \$x = \$x_s*\$x_n*\$pi/\$x_d; \$deriv1 =(\$a*(sin(\$x)+cos(\$x))+ \$a*\$x*(cos(\$x)-sin(\$x))); \$funct1 ="(\$a*(sin(x)+cos(x))+ \$a*x*(cos(x)-sin(x)))"; TEXT(EV2(<