Differentiate Cos^-1 [ x-x^-1/ x+ x^-1] w r t x - Maths - Continuity and Differentiability

Question

Differentiate Cos^-1 [ x-x^-1/ x+ x^-1] w r t x

Varun.Rawat · Accepted Answer

Let y = cos-1x - x-1x+x-1⇒y = cos-1x - 1xx + 1x⇒y = cos-1x2 - 1x2 + 1Put x = tan θNow, y = cos-1tan2θ - 1tan2θ + 1⇒y = cos-1-1 - tan2θ1 + tan2θ⇒y = cos-1- cos 2θ⇒y = cos-1cosπ+2θ⇒y =π+2θ⇒y = π + 2 tan-1x⇒dydx = 0 + 21+ x2 = 21+ x2

Differentiate Cos^-1 [ x-x^-1/ x+ x^-1] w.r.t x