The two main Trigonometric Derivatives that you will need to know are:
d(sinx)/dx=cosx
d(cos)/dx=-sinx
However there are several others (tanx, cotx, secx, cscx) that are also useful to memorize.
Derivatives of Trigonometric Functions (cr: Organic Chemistry Tutor)
You will see functions that look like: sin2x and may wonder how to derive/solve these. We will be discussing this in lesson 2.6, chain rule.