The \(m-\)th derivative of the \(n-\)th order Bernstein polynomial of a function \(f\) is considered for large values of \(n\). For functions \(f\) satisfiyng a certain Lipschitz condition the asymptotics is done by using the Gauss-Weierstrass singular integral. So-called overdifferentiation formulae are derived, involving \(p\) times differentiated Bernstein polynomials of functions that are not \(C^p\).