Questions: Find y′. y=4 sin x cos x y′=

Find y′. y=4 sin x cos x y′=
Transcript text: Find $y^{\prime}$. \[ y=4 \sin x \cos x \] \[ y^{\prime}= \]
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Solution

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Solution Steps

Step 1: Differentiate the Function

To find \( y^{\prime} \) for the function \( y = 4 \sin x \cos x \), we apply the product rule and the double angle identity. The derivative is calculated as follows:

\[ y^{\prime} = -4 \sin^2 x + 4 \cos^2 x \]

Step 2: Simplify the Derivative

Using the double angle identity, we can simplify the expression for the derivative:

\[ y^{\prime} = 4 \cos(2x) \]

Final Answer

The derivative of the function is

\[ \boxed{y^{\prime} = 4 \cos(2x)} \]

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