Differential analysis is nothing but marginal costing. It involves analyzing what gain/loss we will receive by implementing a particular alternative. It is very helpful in deciding what alternative to choose when deciding between various alternatives.
It considers common costs that will be incurred irrespective of the alternative implemented as irrelevant cost whereas costs that will be incurred only if a particular alternative is implemented is considered as relevant costs. It is very useful in analyzing whether any additional order should be accepted, pricing for such orders, whether to shut down or not, etc.