Question

Find the derivative of the following functions: $\sin x\cos x$

Answer 1

Let $f\left(x\right)=\sin x\cos x$
Thus using product rule,
$f^{\prime }\left(x\right)=\sin x(-\sin x)+\cos x\left(\cos x\right)$

$={\cos }^{2}x-{\sin }^{2}x$

$=\cos 2x$