88## DBsection(Chain rule (with trigonometric functions))
99## Date(05/11/2018)
1010## Institution(Colorado Community College System)
11- ## Author(Eric Fleming)
11+ ## Author(Eric Fleming-updated to use Composition_Ans by Brittni Lorton August 2022 )
1212## MO(1)
1313## KEYWORDS('chain rule', 'trig', 'trigonometric functions', 'tan', 'tangent', 'tan(x)', 'sec', 'secant', 'sec(x)')
1414
@@ -40,7 +40,6 @@ $a=random(2,9,1);
4040$b=random(2,20,1);
4141$c=random(2,20,1);
4242
43-
4443$f=Formula("tan(sec($a x))");
4544
4645$ans1=Formula("tan(u)");
@@ -50,35 +49,23 @@ $ans3=Formula("$a sec^2(sec($a x)) sec($a x) tan($a x)");
5049###########################
5150# Main text
5251
53- # BEGIN_PGML
52+ BEGIN_PGML
5453
55- # Decompose [`\displaystyle y=[$f]`] into two functions [`y=f(u)`] and [`u=g(x)`] such that [`y=f(g(x))`]. Then find `\frac{dy}{dx}`.
54+ 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}`.
5655
57- # [`f(u)=`][_______________] [@ AnswerFormatHelp("formulas") @]*
56+ [`f(u)=`][_______________] [@ AnswerFormatHelp("formulas") @]*
5857
59- # [`g(x)=`][_______________] [@ AnswerFormatHelp("formulas") @]*
58+ [`g(x)=`][_______________] [@ AnswerFormatHelp("formulas") @]*
6059
61- #`\frac{dy}{dx}=`[_______________] [@ AnswerFormatHelp("formulas") @]*
60+ END_PGML
6261
63- #END_PGML
64- Context()->texStrings;
65- BEGIN_TEXT
66- Decompose \( y=$f\) into two functions \(y=f(u)\) and \(u=g(x)\) such that \(y=f(g(x))\). Then find \( \frac{dy}{dx}\).
67- $BR
68- $BR
69- \( f(u) \) = \{ ans_rule(20) \}
70- \{ AnswerFormatHelp("formulas") \}
71- $BR
72- \( g(x) \) = \{ ans_rule(20) \}
73- $BR
74- END_TEXT
75- Context()->normalStrings;
7662COMPOSITION_ANS( $ans1, $ans2, vars=>['u','x'], showVariableHints=>1);
63+ BEGIN_PGML
64+
65+ `\frac{dy}{dx}=`[_______________]{$ans3} [@ AnswerFormatHelp("formulas") @]*
66+
67+ END_PGML
7768
78- BEGIN_TEXT
79- \(\frac{dy}{dx}= \) \{ans_rule(20)\}
80- END_TEXT
81- ANS( $ans3->cmp() );
8269
8370############################
8471# Solution
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