We study the dynamics and dynamic scattering functions of a semiflexible polymer of persistence length /(p) in the limit q/(p) much greater than 1, taking into account the inextensibility of the polymer chain and the effects of hydrodynamics. We find two distinct contributions to the scattering functions with different scaling behaviors in q(2)t(3/4) and q(2)t(7/8) coming from the anisotropic dynamics of the polymer. We also calculate the initial decay of the dynamic structure factor and obtain a novel t log t decay which allows us to explain recent dynamic light scattering experiments on viral particles.