# What is the derivative of k(x)=sin x cos x?

if: $k \left(x\right) = f \left(x\right) g \left(x\right)$
$k ' \left(x\right) = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$
$k ' \left(x\right) = \cos \left(x\right) \cos \left(x\right) + \sin \left(x\right) \left(- \sin \left(x\right)\right) =$
$= {\cos}^{2} \left(x\right) - {\sin}^{2} \left(x\right) = \cos \left(2 x\right)$