# How do you find the derivative of  f(x)= (1/2) sin(2x) + cos(x) ?

$f ' \left(x\right) = \cos 2 x - \sin x .$
Given that $f \left(x\right) = \left(\frac{1}{2}\right) \sin 2 x + \cos x .$
$\therefore f ' \left(x\right) = \left(\frac{1}{2}\right) \left(\sin 2 x\right) ' + \left(\cos x\right) '$
$\therefore f ' \left(x\right) = \left(\frac{1}{2}\right) \left(\cos 2 x\right) \left(2 x\right) ' + \left(- \sin x\right) = \left(\frac{1}{2}\right) \left(2\right) \cos 2 x - \sin x = \cos 2 x - \sin x .$