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

Question

Differentiate with respect to x :

tan-1 ( a - x / 1 + ax )

The answer: -1 / ( 1 + x2 )

Manbar Singh · Accepted Answer

Let y = tan-1a-x1 + axput a = tan α   and  x = tan βNow, y = tan-1tan α - tan β1 + tan α 
 tan β⇒y = tan-1tanα - β⇒y = α - β⇒y = tan-1a - tan-1x⇒dydx = 0 - 11 + x2⇒dydx = -11 + x2