If $y={\tan }^{-1}\left(\frac{3\cos x-4\sin x}{4\cos x+3\sin x}\right)+2{\tan }^{-1}\left(\frac{x}{1+\sqrt{1-{x}^{2}}}\right)$then $\frac{dy}{dx}$ at $x=\frac{\sqrt{3}}{2}$ is equal to: [JEE Main 2026, 4 Apr (Shift 1)]

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If \(y={\tan }^{-1}\left(\frac{3\cos x-4\sin x}{4\cos x+3\sin x}\right)+2{\tan }^{-1}\left(\frac{x}{1+\sqrt{1-{x}^{2}}}\…

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