Differentiate with respect to x :

cot-1 ( 1 + x / 1 - x )

The answer : -1 / 1 + x2

Let y = cot-11+x1-xput x = tan θNow, y = cot-11 + tan θ1 - tan θy = cot-1tanπ/4 +  tan θ1 - tanπ/4   tan θy = cot-1tanπ4 + θy = cot-1cotπ2 - π4 + θy = π4 - θy = π4 - tan-1xdydx = 0 - 11+x2dydx = -11+x2

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