Another look at the rules of differentiation

It is an eye opening experience for students to find out that even a great mathematician like Leibniz made mistakes, forgot to check carefully his calculations, and was temporarily misled by user-friendly but incorrect formulas. From Leibniz's mishap with the derivation of the rules of differentiation students can learn the importance of spending time critically revising their work and the fact that trying to correct a mistake can sometimes produce new insights.