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I can get an answer with Mathematica or something but I have no idea how to actually do this. I don't know how fundamental theorem of calculus can be applied. (if it can be)

[itex]\Phi[/itex]((log(S/K)+(r+σ^2)T)/(σ sqrt(T)))

where phi is the std normal cdf.

I'm doing option pricing analysis but I can't really figure out how to derive this with respect to r or sigma or any other parameter. I would appreciate any help.