# What is the derivative of  f(x)=xcos(cosx))?

$f ' \left(x\right) = \cos \left(\cos x\right) + x \sin \left(\cos x\right) \sin x$
$f \left(x\right) = x \cos \left(\cos x\right)$
$f ' \left(x\right) = \left(x \cos \left(\cos x\right)\right) ' = \cos \left(\cos x\right) - x \sin \left(\cos x\right) \left(\cos x\right) ' = \cos \left(\cos x\right) + x \sin \left(\cos x\right) \sin x$