In this paper under review, the authors study the sign of \(Z^{(k)}(t)Z^{(l)}(t)\) and \(Z^{(k)}(t)Z^{(l)}(t)Z^{(m)}(t)Z^{(n)}(t)\), where \(Z^{(k)}(t)\) is the \(k\)th derivative of the Hardy function defined by \[ Z(t):=e^{i\theta(t)}Z\left(\frac{1}{2}+it\right)=\left(\pi^{-it}\frac{\Gamma\left(\frac{1}{4}+\frac{it}{2}\right)}{\Gamma\left(\frac{1}{4}-\frac{it}{2}\right)}\right)^{1/2}\zeta\left(\frac{1}{2}+it\right) \] and \(\zeta\) denotes the Riemann zeta function. For instance, in Theorem 1, they prove for \(k=0\) and \(l=2\) that \[ \mathrm{meas}\left\{t\in{[T,2T]}: Z(t)Z''(T)<0\right\}\geq\left(\frac{3}{25}+o(1)\right)T. \] In Theorem 2, similar result is proved in the case when \(k+l\) is even and \(k\equiv l+2\pmod 4\).