  Using a result of Robertson \textit{[Proc. Edinburgh Math. Soc. (2), 1976]},
we introduce a notion of differentiation of maps on certain classes of unital
commutative C*-algebras. We then derive C*-algebraic Gauss-Lucas theorem and
formulate C*-algebraic Sendov's conjecture. We verify C*-algebraic Sendov's
conjecture for polynomials of degree 2.
