On the derivative of a polynomial

If p ( z ) = Σ v = 0 n a v z v p(z) = \Sigma _{v = 0}^n {{a_v}{z^v}} is a polynomial of degree n n having all its zeros in | z | ≦ K ≦ 1 |z| \leqq K \leqq 1 , then it is known that max | z | = 1 | p ′ ( z ) | ≧ ( n / ( 1 + K ) ) max | z | = 1 | p ( z ) | {\max _{|z| = 1}}|p’(z)| \geqq (n/(1 + K)){\max _{|z| = 1}}|p(z)| . In this paper we consider the case when K > 1 K > 1 and obtain a sharp result.