Question about derivation and normal distribution

Hello,
I have the following function:

C(S,t):=S*N(d1)-K*exp(-r*(T-t))*N(d2)

where N(d1) is the normal cumulative distribution with d1 as parameter.

I am trying to use maxima in order to compute a first-order partial
derivative of the above C(S,t) function as follows:

diff(C(S,t),t)

I don't know how to express the cumulative normal distribution nor how to
derivate it.

Can anyone please help?

Thanks in advance,

Julien.