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)

Question

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)

anonymous · Answer

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.

anonymous · Answer

Thanks creeksider!!

anonymous · Answer

Try to use Method of Substitution here x=cos2A will work

anonymous · Answer

@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.