Applied Math Seminar Announcement

 
The Product Rule is a common rule used on Calculus which states that (f*g)'=f'g+fg'. However, a common mistake made by Calculus I students is to assume that (f*g)'=f'g'. We pose the question, for what types of functions does this equality hold? In more general terms, when does the equality (f*g)⁽ⁿ⁾=f⁽ⁿ⁾g⁽ⁿ⁾ hold? We find that a large class of function pairs satisfy this equality, including a large class of slowly varying functions.