Difference between revisions of "DifferentiatingFormulas"

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(New page: <h2>Differentiating Formulas: PG Code Snippet</h2> <!-- Header for these sections -- no modification needed --> <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;"...)
 
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{{historical}}
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<p style="font-size: 120%;font-weight:bold">This problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/DiffCalc/DifferentiateFunction.html a newer version of this problem]</p>
 
<h2>Differentiating Formulas: PG Code Snippet</h2>
  
<h2>Differentiating Formulas: PG Code Snippet</h2>
   
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<p>
  
<p>
 
<b>Initialization:</b>
  
<b>Initialization:</b>
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In the initialization section, we need to include the macro file <code>MathObjects.pl</code>.
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In the initialization section, we need to include the macro file <code>MathObjects.pl</code> or be using a parser that loads MathObjects.pl automatically.
 
</p>
  
</p>
 
</td>
  
</td>
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$fxa = $fx->eval(x=>"$a");
  
$fxa = $fx->eval(x=>"$a");
 
$fy = $f->D('y');
  
$fy = $f->D('y');
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$fxy = $fx->D('y');
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$fyx = $fy->D('x')->reduce;
 
</pre>
  
</pre>
 
</td>
  
</td>
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x to be a variable, so we add the variable y to the context.
  
x to be a variable, so we add the variable y to the context.
 
Then, we use the partial differentiation operator <code>D('var_name')</code>
  
Then, we use the partial differentiation operator <code>D('var_name')</code>
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to take a partial derivative with respect to that variable.
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to take a partial derivative with respect to that variable. We can use the evaluate
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feature as expected.
 
</p>
  
</p>
 
</td>
  
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\( f_y(x,y) \) = \{ans_rule(20)\}
  
\( f_y(x,y) \) = \{ans_rule(20)\}
 
$PAR
  
$PAR
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\( f_{xy} (x,y) \) = \{ans_rule(20)\}
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\( f_{yx} (x,y) \) = \{ans_rule(20)\}
 
END_TEXT
  
END_TEXT
 
Context()->normalStrings;
  
Context()->normalStrings;
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<td style="background-color:#eeddff;border:black 1px dashed;">
  
<td style="background-color:#eeddff;border:black 1px dashed;">
 
<pre>
  
<pre>
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ANS( $fx->cmp() );
  
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$showPartialCorrectAnswers=1;
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ANS( $fx ->cmp() );
 
ANS( $fxa->cmp() );
  
ANS( $fxa->cmp() );
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ANS( $fy->cmp() );
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ANS( $fy ->cmp() );
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ANS( $fxy->cmp() );
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ANS( $fyx->cmp() );
   
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ENDDOCUMENT;
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ENDDOCUMENT();
 
</pre>
  
</pre>
 
<td style="background-color:#eeccff;padding:7px;">
  
<td style="background-color:#eeccff;padding:7px;">
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[[Category:Problem Techniques]]
  
[[Category:Problem Techniques]]
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<ul>
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<li>[http://webwork.maa.org/wiki/Introduction_to_MathObjects Introduction_to_MathObjects]</li>
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</ul>

Latest revision as of 08:20, 28 June 2023

This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with a newer version of this problem

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


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