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Mathematics Question on Derivatives

Differentiate tan−1(1+x2−1x) w.r.t  cos−1((1+1+x2)2(i+x2))tan^{-1}(\frac{\sqrt{1+x^2}-1}{x}) \,w.r.t\,\,cos^{-1}(\frac{\sqrt(1+\sqrt{1+x^2})}{2\sqrt({i}+x^2)})

Answer

The derivative of tan−1(1+x2−1x) w.r.t  cos−1((1+1+x2)2(i+x2))  is  −12tan^{-1}(\frac{\sqrt{1+x^2}-1}{x}) \,w.r.t\,\,cos^{-1}(\frac{\sqrt(1+\sqrt{1+x^2})}{2\sqrt({i}+x^2)})\,\ is \,\,-\frac{1}{2}.