# How do you use the product rule to differentiate y=cos(x)*sin(x) ?

$y = u \cdot v = \cos \left(x\right) \cdot \sin \left(x\right)$
$u ' = - \sin \left(x\right)$
$v ' = \cos \left(x\right)$
$y ' = \left(u v\right) ' = u ' v + u v ' = - \sin \left(x\right) \cdot \sin \left(x\right) + \cos \left(x\right) \cdot \cos \left(x\right)$
$y ' = \left(u v\right) ' = u ' v + u v ' = - {\sin}^{2} \left(x\right) + {\cos}^{2} \left(x\right)$