## DESCRIPTION ## Calculus ## ENDDESCRIPTION ## KEYWORDS('derivative' 'implicit') ## Tagged by tda2d ## DBsubject('Calculus') ## DBchapter('Differentiation') ## DBsection('Implicit Differentiation') ## Date('') ## Author('') ## Institution('Union College') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') DOCUMENT(); loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGunion.pl", # Union College utilities "PGcourse.pl", # Customization file for the course ); TEXT(beginproblem()); BEGIN_PROBLEM(); $x0 = non_zero_random(-2,2,1);$y0 = non_zero_random(-2,2,1); $a = random(2,6,1);$b = random(2,4,1); while (3*$b*$y0**2 - 4*($a*$x0 - $y0)**3 == 0) {$b = random(2,4,1); } $c = ($a*$x0-$y0)**4 + $b*$y0**3; BEGIN_TEXT For the equation given below, evaluate $$\displaystyle\frac{dy}{dx}$$ at the point $$(x0,y0)$$: $(a x - y)^4 + b y^3 = c.$ $PAR $$\displaystyle\frac{dy}{dx}$$ at $$(x0,y0)$$ = \{ans_rule(20) \} END_TEXT$showPartialCorrectAnswers = 1; $ans = (-4*$a*($a*$x0-$y0)**3)/(3*$b*$y0**2 - 4*($a*$x0 -$y0)**3); ANS(num_cmp(\$ans)); END_PROBLEM(); ENDDOCUMENT();