How do I compute the derivative \frac{\partial X_t}{\partial \sigma}? Where dX_t=\theta (\muX_t)dt+\sigma \sqrt{X_t}dZ_t
You may want to see Kunita's "Stochastic Flows and Stochastic Differential Equations". Among other things, he develops a calculus of semimartingales with spatial parameters there, and discusses smoothness and differentiation with respect to parameters. 

