My Math Forum Derivative with a range constraint

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 June 11th, 2010, 06:45 AM #1 Newbie   Joined: Jun 2010 Posts: 11 Thanks: 0 Derivative with a range constraint I have the following question: x=sin(a) / cos(b) a+b < pi/2 a>0, b>0 0
 June 11th, 2010, 07:57 AM #2 Senior Member   Joined: Jan 2009 Posts: 344 Thanks: 3 Re: Derivative with a range constraint If you need to clarify/check you work/answers, there is a great http://www.wolframalpha.com/ to do this.
 June 11th, 2010, 08:03 AM #3 Newbie   Joined: Jun 2010 Posts: 11 Thanks: 0 Re: Derivative with a range constraint Yes I know about Wolfram but that just confirms my calculation. I suspect the range isnt being taken into account but cant see where
 June 12th, 2010, 09:16 AM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,929 Thanks: 1124 Math Focus: Elementary mathematics and beyond Re: Derivative with a range constraint I don't see it either. $x\,=\,\frac{\sin{a}}{\cos{b}}\,\Rightarrow\,a\,=\, \sin^{-1}\left(x\cos{b}\right)$ so $\frac{da}{dx}\,=\,\frac{\cos{b}}{\sqrt{1\,-\,x^2\cos^2{b}}}\,\ne\,\frac{\cos^3{b}\cos{a}}{\co s{(a\,+\,b)}\cos{(a\,-\,b)}}$

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