##DESCRIPTION
#  First Created: 6/2/00
#  Last Modified: 6/2/00
#  Author: Joseph Neisendorfer
#  WebworK Entry: Robert Van Dam
#  Location: University of Rochester
#
#  Math 164 Problems - Assignment 5 - Problem 11
##ENDDESCRIPTION

##KEYWORDS('vector', 'partial', 'derivative')

DOCUMENT();

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = random(1, 5);
$b = random(-5, 5);

$dfdx = -$b/(2*$a);
$dfdy = $b/(2*$a);
$dfdz = $PI/4;

BEGIN_TEXT
$PAR
Find the first partial derivatives of \( f(x,y,z) = z \ \arctan(\frac{y}{x}) \) at
the point ($a, $a, $b).
$PAR
A. \( \frac{\partial f}{\partial x}($a, $a, $b) = \) \{ ans_rule(30) \}
$PAR
B. \( \frac{\partial f}{\partial y}($a, $a, $b) = \) \{ ans_rule(30) \}
$PAR
C. \( \frac{\partial f}{\partial z}($a, $a, $b) = \) \{ ans_rule(30) \}
END_TEXT
ANS(num_cmp($dfdx));
ANS(num_cmp($dfdy));
ANS(num_cmp($dfdz));

ENDDOCUMENT();