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Differentiate \(tan^{-1}(\frac{\sqrt{1-x^2}}{x})\)with respect to \(cos^{-1}(2x\sqrt{1-x^2}),\) when x ≠ 0.

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Let u = \(tan^{-1}(\frac{\sqrt{1-x^2}}{x})\) and 

v = \(cos^{-1}(2x\sqrt{1-x^2})\)

We have to determine \(\frac{du}{dv}\)

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