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for random functions u , v we have (u o v)'= (u' o v).v' (uv)'=u'v+v'u (u/v)'=(u'v-v'u)/v² (u^n)'=nu'u^(n-1) (exp u)'=u'exp u (ln u)'= u'/u okay now all you have to do is practice .until you master it. PS: (u o v) means u(v(x)) for any x. and (something)' = derivative of something.

A first way for that is to look the invertible elements of the rings .