As described in this documentation link, 'mdlDerivatives' is an optional method that can be used to compute the derivatives for the continuous states of an S-function at each time step:
'mdlOutputs' is a required method that computes the outputs for an S-function block at each time step
Regarding how the sections of an S-function relate to each other, the following documentation page provides some useful information on how S-functions work and it also describes how the inputs, outputs and states of a block are related:
