Differentiating Formulas

This shows how to check "arbitrary" conditions on the student's answer.

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Complete Code

Download file: DifferentiatingFormulas.pg

PG problem file

Explanation

DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');

Preamble

These standard macros need to be loaded. 
Context()->variables->add(y => 'Real');

$a = random(2, 4);
$f = Formula('x^2y');

$fx  = $f->D('x');
$fxa = $fx->substitute(x => $a);
$fy  = $f->D('y');
$fyx = $fy->D('x')->reduce;

Setup

The Numeric context includes the variable x by default, but the variable y must be added to the context.

The differentiation operator D(variable name) is used to take a partial derivative with respect to the variable give for variable name. Note that the differentaion operator returns a MathObject Formula.

The substitute method is used to evaluate the Formula for the partial derivative with respect to x at a particular value.

BEGIN_PGML
Suppose [`f(x) = [$f]`].  Then

a. [``\frac{\partial f}{\partial x} =``] [____]{$fx}

b. [`f_x ([$a],y) =`] [____]{$fxa}

c. [`f_y(x, y) =`] [____]{$fy}

d. [`f_{yx}(x, y) =`] [___]{$fyx}
END_PGML

Statement

This is the problem statement in PGML. 
BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.