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## DBsection(Chain rule (with trigonometric functions))
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## Date(05/11/2018)
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## Institution(Colorado Community College System)
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- ## Author(Eric Fleming)
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+ ## Author(Eric Fleming-updated to use Composition_Ans by Brittni Lorton August 2022 )
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## MO(1)
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## KEYWORDS('chain rule', 'trig', 'trigonometric functions', 'tan', 'tangent', 'tan(x)', 'sec', 'secant', 'sec(x)')
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@@ -40,7 +40,6 @@ $a=random(2,9,1);
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$b=random(2,20,1);
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$c=random(2,20,1);
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-
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$f=Formula("tan(sec($a x))");
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$ans1=Formula("tan(u)");
@@ -50,35 +49,23 @@ $ans3=Formula("$a sec^2(sec($a x)) sec($a x) tan($a x)");
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###########################
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# Main text
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- # BEGIN_PGML
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+ BEGIN_PGML
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- # Decompose [`\displaystyle y=[$f]`] into two functions [`y=f(u)`] and [`u=g(x)`] such that [`y=f(g(x))`]. Then find `\frac{dy}{dx}`.
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+ Decompose [`\displaystyle y=[$f]`] into two functions [`y=f(u)`] and [`u=g(x)`] such that [`y=f(g(x))`]. Then find `\frac{dy}{dx}`.
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- # [`f(u)=`][_______________] [@ AnswerFormatHelp("formulas") @]*
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+ [`f(u)=`][_______________] [@ AnswerFormatHelp("formulas") @]*
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- # [`g(x)=`][_______________] [@ AnswerFormatHelp("formulas") @]*
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+ [`g(x)=`][_______________] [@ AnswerFormatHelp("formulas") @]*
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- #`\frac{dy}{dx}=`[_______________] [@ AnswerFormatHelp("formulas") @]*
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+ END_PGML
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- #END_PGML
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- Context()->texStrings;
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- BEGIN_TEXT
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- Decompose \( y=$f\) into two functions \(y=f(u)\) and \(u=g(x)\) such that \(y=f(g(x))\). Then find \( \frac{dy}{dx}\).
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- $BR
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- $BR
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- \( f(u) \) = \{ ans_rule(20) \}
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- \{ AnswerFormatHelp("formulas") \}
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- $BR
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- \( g(x) \) = \{ ans_rule(20) \}
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- $BR
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- END_TEXT
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- Context()->normalStrings;
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COMPOSITION_ANS( $ans1, $ans2, vars=>['u','x'], showVariableHints=>1);
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+ BEGIN_PGML
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+
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+ `\frac{dy}{dx}=`[_______________]{$ans3} [@ AnswerFormatHelp("formulas") @]*
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+
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+ END_PGML
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- BEGIN_TEXT
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- \(\frac{dy}{dx}= \) \{ans_rule(20)\}
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- END_TEXT
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- ANS( $ans3->cmp() );
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############################
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# Solution
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