In this talk I will explain why thinking about formal power series is useful, and what they can do for you. I will tell how to write down the coefficents of formal power series that take the form of exponential generating functions $E_g(E_{f_1}(x), \dots , E_{f_q}(x))$, using partitions. I will use those results with the added structure provided by thinking about my formal power series as Taylor series of functions to provide a formula for the derivatives of composite functions that look like $g(f_1(x), \dots , f_q(x))$. This talk will be accessible to all graduate students (first years included!) and no prior knowledge of combinatorics is required.