Differentiate tan-1 [ (root 1 - x2) / x ] w.r.t. cos-1 [2x (root 1 - x2)]. Share with your friends Share 19 Manbar Singh answered this Let u = tan-11-x2xput x = cos θ u = tan-11-cos2θcosθ⇒u = tan-1sin θcos θ⇒u = tan-1tan θ⇒u = θ⇒u = cos-1x⇒dudx = -11-x2 Let v = cos-12x1-x2put x = sin θso, v = cos-12 sin θ 1 - sin2θ⇒v = cos-12 sin θ cos θ⇒v = cos-1sin 2θ⇒v = cos-1cosπ2-2θ⇒v = π2-2θ⇒v = π2-2sin-1x⇒v = -21-x2Now,dudv = dudx ×dxdv = -11-x2×-1-x22 = 12 115 View Full Answer