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--- mathematics:derivative_arcsecant [2017/05/16 00:14] – created oemb1905
+++ mathematics:derivative_arcsecant [2019/08/14 19:53] (current) – removed oemb1905
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-A student came to me today with a simple question about the proof in the Finney book regarding arcsecant.  On p.168, Finney (2006) argues that "the absolute value symbol ... eliminates the + / - ambiguity."  The problem is, however, that the absolute value was not due to the piecewise function that was listed, but was due to the implicit derivative of sec y = |x|, not x, as the book states.  It is true, that when we write the function, we write "sec y = x," however this is referring to the unit triangle with an angle y, and thus the hypotenuse is x, but since the hypotenuse cannot be negative, we must, even at the top of p.168, write |x|, not simply x.  Therefore, there are two errors in the text.  I propose the following correction and proof instead using the restrictions of the domain and range.  See enclosed.  Thanks to my student, Alexander Ortiz, for bringing this up!
-<a target="_blank" href="http://ic.pics.livejournal.com/oemb1905/19468200/310531/310531_original.jpg"><img src="http://ic.pics.livejournal.com/oemb1905/19468200/310531/310531_original.jpg" alt="Derivative of Arcsecant" title="Derivative of Arcsecant" width="550" /></a>

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