Difference between revisions of "DifferentiatingFormulas"
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$fxa = $fx->eval(x=>"$a"); |
$fxa = $fx->eval(x=>"$a"); |
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$fy = $f->D('y'); |
$fy = $f->D('y'); |
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| − | $ |
+ | $fyx = $fy->D('x')->reduce; |
</pre> |
</pre> |
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</td> |
</td> |
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| Line 61: | Line 61: | ||
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. |
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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. |
+ | to take a partial derivative with respect to that variable. We can use the evaluate |
| + | feature as expected. |
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</p> |
</p> |
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</td> |
</td> |
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\( f_y(x,y) \) = \{ans_rule(20)\} |
\( f_y(x,y) \) = \{ans_rule(20)\} |
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$PAR |
$PAR |
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| − | \( f_{ |
+ | \( f_{yx} (x,y) \) = \{ans_rule(20)\} |
END_TEXT |
END_TEXT |
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Context()->normalStrings; |
Context()->normalStrings; |
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| Line 98: | Line 98: | ||
<td style="background-color:#eeddff;border:black 1px dashed;"> |
<td style="background-color:#eeddff;border:black 1px dashed;"> |
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<pre> |
<pre> |
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| − | ANS( $fx->cmp() ); |
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| + | $showPartialCorrectAnswers=1; |
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| + | |||
| + | ANS( $fx ->cmp() ); |
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ANS( $fxa->cmp() ); |
ANS( $fxa->cmp() ); |
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| − | ANS( $fy->cmp() ); |
+ | ANS( $fy ->cmp() ); |
| − | ANS( $ |
+ | ANS( $fyx->cmp() ); |
| − | ENDDOCUMENT; |
+ | ENDDOCUMENT(); |
</pre> |
</pre> |
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<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> |
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Revision as of 22:08, 3 March 2010
Differentiating Formulas: PG Code Snippet
This PG code shows how to differentiate a MathObjects Formula.
| PG problem file | Explanation |
|---|---|
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", ); TEXT(beginproblem()); |
Initialization:
In the initialization section, we need to include the macro file |
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 |
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. |
