Derived functor of a homotopical functor

Exercise 6.6.6. Let \(F\colon C \to D\) be a functor which inverts all morphisms in \(W\). By the universal property of \(C[W^{-1}]\), \(F\) factors through a functor \(\bL F \colon C[W^{-1}] \to D\). Show that \(\bL F\) is a total left derived functor of \(F\).