We have already addressed the topic of implicit functions in Chap. 23 : In practice, functions are often not given by explicit specification of the mapping rule, but implicitly determined by an equation. We encountered this problem several times in the solutions of differential equations. In this chapter, we provide a method for dealing with implicit functions. For example, under certain conditions, it will be possible to determine the derivative of an implicit function at a point x without knowing an explicit mapping rule of this function.