In this paper the author discusses the simultaneous approximation of a function and of its derivatives in weighted \(L^p\) spaces. Both trigonometric polynomial approximation and algebraic polynomial approximation are discussed. In the case of trigonometric polynomial approximation the weight function is supposed to belong to the Muckenhoupt class. By a simple relation between the weight functions the trigonometric polynomial approximation and the algebraic polynomial approximation are interrelated. Properties of the weight functions in the trigonometric and in the algebraic case are also discussed.