On the value distribution of ff^(k)

Let f be a transcendental entire function. In this paper we will prove that if f is of finite order, then there exists at most one integer k≥2 such that ff^(k) may have non-zero and finite Picard exceptional value. We also give a class of entire functions which have no non-zero finite Picard values. If f is a transcendental meromorphic function, we obtain that for non-negative integers n, n₁, ..., n_k with n≥1, n₁+...+n_k≥1, if δ(o,f)>3/(3n+3n₁+...+3n_k+1), then fⁿ(f^l)ⁿ¹...(f^k)^nk has no finite non-zero Picard values