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Suppose that A = C([0,1]) and d(f) = ([d/dt])f(t) = f¢(t) with the domain D(d) = C1([0,1]) where C1([0,1]) is the algebra of all continuously differentiable functions on [0,1]. ||d(xn) || = n = n ||xn|| implies that d is an unbounded derivation from D(d) into A. If fn Î D(d), fn ® f Î A , and d(fn) ® g, then f¢n ® g uniformly on [0,1] and fn(0) ® f(0). So g is differentiable and f¢ = g. Therefore f Î D(d) and d(f) = g.