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Topic: [ap-calculus] Derivatives of Inverse trig functions
Replies: 1   Last Post: Dec 1, 2010 8:21 AM

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Benjamin Goldstein

Posts: 434
Registered: 9/6/09
RE: [ap-calculus] Derivatives of Inverse trig functions
Posted: Dec 1, 2010 8:21 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

The answer to this question is yes. Students do need to know the
derivatives of the inverse trig functions, at least of arcsine, arccosine,
and arctangent. (The others have never shown up on a released exam
question.)

Most recently, 2008 AB #26 asked students to find the tangent line to y =
arctan(4x) at a given x-coordinate. I suppose students would be free to
convert this equation to tan(y) = 4x and find a derivative implicitly, but
the most direct way is to know the derivative of the arctangent function.

Other questions involving differentiating inverse trig functions...
1985 AB #20, 1993 BC #26, and AB #28 and BC #18 from the sample exams

Free response 2006 BC #3 also involved an arcsine, but that question was
calculator active; the question could be answered using nDeriv.

You might notice a long drought between the last time a released,
calculator-inactive question dealt with differentiating inverse trig
functions (1993) and when we started to see them again (the sample exams
were first released in 2007, I believe). If you had asked this question
before the sample exam was released, I would have said that it didn't look
like AP Exam was testing inverse trig derivatives anymore. But now it
seems pretty clear that the test committee sees these derivatives as fair
game.

Cheers,
Benjamin Goldstein
The Cambridge School of Weston
Weston, MA

-----Original Message-----
From: Tonya Lackey [mailto:tlackey@lakeplacidcsd.net]
Sent: Tuesday, November 30, 2010 1:01 PM
To: AP Calculus
Subject: [ap-calculus] Derivatives of Inverse trig functions

Do the students need to memorize the rules for derivatives of inverse trig
functions for the AP exam - AB? Or will they be given? Or do they not
even show up on the AB exam?

Thanks
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