DifferentiatingFormulas

Differentiating Formulas: PG Code Snippet

This PG code shows how to differentiate a MathObjects Formula.

Problem Techniques Index

PG problem file	Explanation
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", ); TEXT(beginproblem());	Initialization: In the initialization section, we need to include the macro file MathObjects.pl or be using a parser that loads MathObjects.pl automatically.
Context("Numeric")->variables->add(y=>"Real"); $a = random(2,4,1); $f = Formula("x*y^2"); $fx = $f->D('x'); $fxa = $fx->eval(x=>"$a"); $fy = $f->D('y'); $fyx = $fy->D('x')->reduce;	Setup: The Numeric context automatically defines x to be a variable, so we add the variable y to the context. Then, we use the partial differentiation operator D('var_name') to take a partial derivative with respect to that variable. We can use the evaluate feature as expected.
Context()->texStrings; BEGIN_TEXT Suppose \( f(x) = $f \). Then $PAR \( \displaystyle \frac{\partial f}{\partial x} \) = \{ans_rule(20)\} $PAR \( f_x ($a,y) \) = \{ans_rule(20)\} $PAR \( f_y(x,y) \) = \{ans_rule(20)\} $PAR \( f_{yx} (x,y) \) = \{ans_rule(20)\} END_TEXT Context()->normalStrings;	Main Text: The problem text section of the file is as we'd expect.
$showPartialCorrectAnswers=1; ANS( $fx ->cmp() ); ANS( $fxa->cmp() ); ANS( $fy ->cmp() ); ANS( $fyx->cmp() ); ENDDOCUMENT();	Answer Evaluation: As is the answer.

Problem Techniques Index

• Introduction_to_MathObjects