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What is the second derivative of Sin²x​
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[tex]\textbf{First derivative:}\\\\~~\dfrac{d}{dx}(\sin^2 x) \\\\\\= 2 \sin x \cdot \dfrac{d}{dx} (\sin x)\\\\\\=2 \sin x \cos x\\\\\\=\sin 2x\\\\ \textbf{Second derivative:}\\\\\dfrac{d^2}{dx^2} (\sin^2 x)\\\\\\=\dfrac{d}{dx}(\sin 2x)\\\\\\=\cos 2x \dfrac{d}{dx}(2x)\\\\\\=2 \cos 2x\\\\\text{Hence, the second derivative of the given function is}~ 2 \cos (2x).[/tex]
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The second derivative of sin2x is d/dx(sin 2x) = 2 cos 2x.
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