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 2022年亚洲世界杯预选赛 (first years included!) and no prior knowledge of combinatorics is required.