The derivative of \(\rm\csc^{-1}\left({1\over2x^2-1}\right)\) w.r.t. \(\rm\sqrt{1-x^2}\) is:

1
-2 cos-1 x
2
\(\rm{-2\over\cos^{-1} x}\)
3
\(\rm1\over\sqrt{1+2x}\)
4
-2/x

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