In this paper, the value distribution of phi (z)[f(z)]^{n-1}f^{(k)}(z) is studied, where f(z) is a transcendental meromorphic function, phi(z)(≢ 0) is a function such that T(r, phi) = o(T(r, f)) as r → + ∞, n and k are positive integers such that n = 1 or n ≥ k + 3. This generalizes a result of Hiong.