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The derivative of arctan(x - sqrt(x^2 + 1) is [itex]\frac{1}{2(x^2+1)}[/itex]

take arctan(x) to be A and arctan(x-sqrt(x^2 + 1)) to be B.

[itex]A'=\frac{1}{x^2+1}[/itex]

[itex]B'=\frac{1}{2}*A'[/itex]

Why doesn't [itex]\frac{1}{2}*A=B[/itex]?

If you'd like, I can prove the derivative for you, but it's moderately tedious to simplify it to that point.