The derivative of tan-11+x2-1x with respect to tan-12x1-x21-2x2 at x=12 is

put  x=tanθ in the given expressions. tan-11+x2-1x=tan-1secθ-1tanθ=tan-1tanθ2=12θ=12Tan-1x Substitute x=sinα,tan-12x1-x21-2x2=tan-1sin2αcos2α=2α=2sin-1x Derivative of 12Tan-1x w.r.to 2sin-1x We get dfdg=dfdxdgdx=121+x2×1-x22=310, at x=12