The life work of Jacques Derrida was to challenge conventional or accepted meaning, particularly regarding language and symbols and how they create artificial structures. Therefore, his exposure to the writings of Nietzsche and Freud germinated the seeds of Derrida's work, just as their work influenced countless post-modern theorists. (Derrida would argue against and embrace their influence at different times throughout his career.)
Nietzsche's work called into question the foundations on which man evaluates himself and his purpose. By encouraging this kind of questioning, even to the point of embracing madness or nihilism, Nietzsche provided an outlet for those dissatisfied with one of two options: a belief in a supreme being or a belief in social order. Both belief systems imposed a morality that went against man's inherent nature, according to Nietzsche. He believed man could only become self-realized by eliminating weakness in himself and society, thereby becoming a "superman." While Derrida would consider Nietzsche's prescription yet another artifice, the radical suggestion that the social order itself is an artificial construct should be seen as a precursor to deconstructionist theory.
Nietzsche's ideas about self-examination and the genesis of belief influenced Freud a great deal. However, Freud considered psychoanalysis a science and not a philosophy; therefore, he insisted that self-examination should lead to practical applications in one's life. For example, a reflective approach to one's relationship with one's mother could provide key insights into how one operates in the world. In this way, Freud could be seen as the anti-Derrida, in that his theories give rise to a disorder for which he is the only one with a cure. However, in Freud's suggestion that one could disassemble former behavioral patterns and create new meaning, there is an overlap with deconstructionist thought.