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How to calculate the drivative of tan -1 (x/sqrt(1-x^2))? The solution says it set y = as sqrt(x-1) and it gives dy/dx = -1/(2sqrt(x-1)). How is that possible? (Problem 2 18.01, Integration Techniques PDF 5A - 3g)

OCW Scholar - Single Variable Calculus
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This is actually a pretty cool problem, but a tough one, even with the minimal explanation provided in the materials. A full explanation is too long to type here so I wrote it up separately and posted it as a PDF.
Thanks creeksider!!
Try to use Method of Substitution here x=cos2A will work

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@creeksider, I cannot up vote your explanation enough! I was close working it out by myself but lacked confidence that my page of calculations was going anywhere because the given solution seemed so elegant. I kept quitting and starting over. Your write up cured that lack of confidence...for this problem at least! Thank you.

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