I'm looking at the greeks from the Black-Scholes equation (see the table midway down Black?Scholes - Wikipedia, the free encyclopedia) ...

dC/dS = N(d1)

I don't understand this result. It seems like the fact d1 is a function of S is being ignored. It seems like N(d1) is being treated as a constant/independent of S but d1 is ln(S/K) etc etc. What am I misunderstanding?

I do understand the result for d2C/dS2 = dN(d1)/dS because N'(x) is N'(f(S)) so you can use the chain rule.

Thanks very much for helping out! This has been a frustrating Saturday night :-(