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 \(-\sin x\).
\[
\cos ^{2} x-\sin ^{2} x
\]