Find \(\frac{d^2 y}{dx^2}\), if y=2 sin^-1⁡(cos⁡x).(a) 0(b) sin^-1\((\frac{1}{cos⁡x})\)(c) 1(d) -1The question was asked in unit test.My query is from Second Order Derivatives topic in section Continuity and Differentiability of Mathematics – Class 12

Find \(\frac{d^2 y}{dx^2}\), if y=2 sin^-1⁡(cos⁡x).(a) 0(b) sin^-1

1.	Find \(\frac{d^2 y}{dx^2}\), if y=2 sin^-1⁡(cos⁡x).(a) 0(b) sin^-1\((\frac{1}{cos⁡x})\)(c) 1(d) -1The question was asked in unit test.My query is from Second Order Derivatives topic in section Continuity and Differentiability of Mathematics – Class 12
Answer» Correct choice is (a) 0 Best EXPLANATION: Given that, y=2 sin^-1⁡(cos⁡x) \(\FRAC{dy}{DX}=2.\frac{1}{\SQRT{1-cos^2⁡x}}\).-sin⁡x=-2 (∵\(\sqrt{1-cos^2⁡x}\)=sin⁡x) \(\frac{d^2 y}{dx^2}\)=\(\frac{d}{dx} (\frac{dy}{dx})=\frac{d}{dx}\) (-2)=0

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