Rate of growth of polynomials non vanishing inside a circle

For a polynomial P(z)=∑ᵥ₌₀ⁿaᵥzᵛ of degree n having all zeros in |z|≥ k, k≥ 1 Govil et al.[ILLINOIS J. of Math.] proved: |P'(z)|≤ nn|a₀|+k²|a₁|/(1+k²)n|a₀|+2k²|a₁||P(z)|. In this paper besides the refinement of above inequality, we also generalize some well known inequalities.