Yeah, you definitely don't need upper level math to trade. Knowing how to use Black-Scholes is far more important than "how to derive it", wouldn't you agree? Unless you're planning some breakthrough that will lead you on the path to LTCM, why not just use the ingredients we already have? They're enough, and doing simple calculations on a daily basis helps.
You'll find trading is predicting a direction, and how much are you going to risk to bet on that direction? The market already tells you what things are worth, perfectly, but this says nothing about where the price is going to be in the next second. That is the actual challenge, and requires a mathematical mind, yes, but not differential calculus.