What is the second derivative of the function $ y = \sin^2 x $?

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∻Solution by Steps∻ ‖ step 1 ⋮ To find the second derivative of the function $ y = \sin^2 x $, we first compute the first derivative: $ \frac{dy}{dx} = 2 \sin x \cos x = \sin(2x) $. ‖ ‖ step 2 ⋮ Next, we differentiate $ \sin(2x) $ to find the second derivative: $ \frac{d^2y}{dx^2} = 2 \cos(2x) $. ‖ ‖ step 3 ⋮ We can also express this as $ 2 \cos^2 x - 2 \sin^2 x = 2 \cos(2x) $. ‖ ‖ step 4 ⋮ Therefore, the second derivative can be simplified to $ 2 - 4 \sin^2 x $. ‖ ∻Answer∻ ⚹ The second derivative of $ y = \sin^2 x $ is $ 2 \cos(2x) $ or $ 2 - 4 \sin^2 x $. ⚹ ∻Key Concept∻ ⚹ The second derivative measures the curvature of the function, indicating how the slope of the tangent line changes. ⚹ ∻Explanation∻ ⚹ The second derivative provides information about the concavity of the function, which is essential for understanding its behavior. ⚹◊What is the first derivative of the function $ y = \sin^2 x $ at $ x = \frac{\pi}{4} $?⍭ Generate me a similar question◊

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