## DBsubject('Calculus')
## DBchapter('Differentiation in Several Variables')
## DBsection('Partial Derivatives')
## KEYWORDS('calculus')
## TitleText1('Calculus: Early Transcendentals')
## EditionText1('2')
## AuthorText1('Rogawski')
## Section1('14.3')
## Problem1('3')
## Author('JustAsk - Vladimir Finkelshtein')
## Institution('W.H.Freeman')

DOCUMENT();

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

TEXT(beginproblem());

Context()->texStrings;

$a=non_zero_random(-5,5,1);
$a1=$a;
if ($a==1) {$a1=''};
if ($a==-1) {$a1='-'};
$ddy='\frac{\partial}{\partial{y}}';

$context = Context();
$context->variables->add(y=>'Real');
$ans=Formula("$a*x/(y+$a*x)^2")->reduce();
BEGIN_TEXT
\{ textbook_ref_exact("Rogawski ET 2e", "14.3","3") \}
$PAR
Use the Quotient Rule to compute:
$PAR
\($ddy\frac {y}{y+$a1 x}= \) \{ans_rule()\}

$BR
END_TEXT 

Context()->normalStrings;

ANS($ans->cmp);


Context()->texStrings;
SOLUTION(EV3(<<'END_SOLUTION'));
$PAR
$SOL
$BR
We use the Quotient Rule to obtain:
$PAR
\($ddy \frac {y}{y+$a1 x}=\frac{(y+$a1 x)$ddy (y)-y $ddy (y+$a1 x)}{\left(y+$a1 x\right)^2}= \frac{(y+$a1 x)\cdot 1 - y \cdot 1}{\left(y+$a1 x\right)^2}=$ans\)
$BR
END_SOLUTION

ENDDOCUMENT();