Differentiate with respect to x : cot-1 ( 1 + x / 1 - x ) The answer - Maths - Continuity and Differentiability

Question

Differentiate with respect to x :

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

The answer : -1 / 1 + x2

Varun.Rawat · Accepted Answer

Let y = cot-11+x1-xput x = tan θNow, y = cot-11 + tan θ1 - tan θ⇒y = cot-1tanπ/4 +  tan θ1 - tanπ/4   tan θ⇒y = cot-1tanπ4 + θ⇒y = cot-1cotπ2 - π4 + θ⇒y = π4 - θ⇒y = π4 - tan-1x⇒dydx = 0 - 11+x2⇒dydx = -11+x2