** Using WeBWorK **

## DESCRIPTION

## This is Problem 2.4.15 from the APEX Calculus text. It covers differentiation of basic trig functions and the product rule.

## ENDDESCRIPTION

## DBsubject(Calculus - single variable)

## DBchapter(Differentiation)

## DBsection(Product rule (with trigonometric functions))

## Level(2)

## Institution('Valdosta State University')

## Author('S. V. Ault')

## RevisedBy('F. J. Francis')

## TitleText1('APEX Calculus')

## AuthorText1('Hartman')

## EditionText1('3.0')

## Section1('2.4')

## Problem1('15')

## MO(1)

## Keywords('derivative', 'product rule', 'trig functions', 'ULETH-MATH1560', 'ULETH-MATH1565')

###########################

#  Initialization

DOCUMENT();

# Load whatever macros you need for the problem

loadMacros(

  # REQUIRED: Used for basic question and answer operations.

  "PGstandard.pl",

  # REQUIRED: Used for expression parsing.

  "MathObjects.pl",

  # Usually required for proper text formatting.

  "PGML.pl",

  # Used to provide contextual help for how to type inequalities/intervals.

  "AnswerFormatHelp.pl"

);

# Sets up basic problem information.

TEXT(beginproblem());

#############################

#   Setup

#-ULETH-#

Context("Numeric");

$a = random(2,9,1);

$f = Formula("x^{$a}");

$fp = $f->D('x');

$r = random(1,2,1);

if ($r==1) {

  $g = Formula("sin(x)");

  $gp = Formula("cos(x)");

  $ans = Formula("$f*cos(x) + $fp*sin(x)")->reduce();

} else {

  $g = Formula("cos(x)");

  $gp = Formula("-sin(x)");

  $ans = Formula("-$f*sin(x) + $fp*cos(x)")->reduce();

}

$fb = Formula($f*$gp)->reduce();

$gb = Formula($fp*$g)->reduce();

#-ENDULETH-#

#############################

#   Problem Text

#-ULETH-#

BEGIN_PGML

Compute the derivative of the given function.

>>[``f(x) = [$f*$g].``]<<

[`f'(x) = `] [_______________] [@ AnswerFormatHelp("formulas") @]*

END_PGML

#-ENDULETH-#

#############################

#  Solution

#-ULETH-#

BEGIN_PGML_SOLUTION

Use the Product Rule.

[``

  f'(x) = ([$f])([$gp]) + ([$fp])([$g]) =  [$fb] + [$gb]  = [$ans].

``]

END_PGML_SOLUTION

#-ENDULETH-#

#############################

#  Answer evaluation

#-ULETH-#

# Setting this to 1 means that students will receive feedback on whether their

# answers are correct.

$showPartialCorrectAnswers = 0;

#-ENDULETH#

ANS( $ans->cmp() );

#############################

#  Comments

    COMMENT('

    Randomization provides 16 different possible versions of this question.<BR>

    Includes a solution set.<BR>

    Made from a ULETH template.<BR>

    ');

ENDDOCUMENT();