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Evaluate the derivative $\frac{d}{d x} \sin x \cos x$
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1) Use Product Rule to find the derivative of $\sin x \cos x$. The product rule states that $(f g)^{\prime}=f^{\prime} g+f g^{\prime}$.
$\left(\frac{d}{d x} \sin x\right) \cos x+\sin x\left(\frac{d}{d x} \cos x\right)$
2 Use Trigonometric Differentiation: the derivative of $\sin x$ is $\cos x$.
$\cos ^{2} x+\sin x\left(\frac{d}{d x} \cos x\right)$
(3) Use Trigonometric Differentiation: the derivative of $\cos x$ is $-\sin x$.
$\cos ^{2} x-\sin ^{2} x$
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