A Baire two function with non-Borel upper symmetric derivative (Q1098948)

The upper symmetric derivative \(\bar Df\) of the function \(f: R\to R\) (R - the real line) is defined by \[ \bar Df(x)=\limsup_{h\to 0}(f(x+h)-f(x- h))/2h. \] \textit{E. Wajch} [Demonstr. Math. 19, 189-195 (1986; Zbl 0615.26003)] has proved that if f is Baire 1 then \(\bar Df\) is Baire 3. In the present paper it is shown that there exists a Baire 2 function f such that \(\bar Df\) is not Borel measurable. This result answers a problem raised by E. Wajch.