From hot-wire anemometer measurements in active-grid wind-tunnel turbulence we have determined the Reynolds number dependence of the velocity derivative moments, the mean-squared pressure gradient, $\chi$, and the normalized acceleration variance, $a_0$, over the Reynolds number range $100\,{\leq}\,R_\lambda\,{\leq}\,900$. The values of $\chi$ and $a_0$ were obtained from the fourth-order velocity structure functions. The derivative moments show power-law dependence on Reynolds number and the exponent is the same with or without shear. In particular, we find the derivative kurtosis, $K_{\partial u/\partial x }\,{\sim}\,R_\lambda^{0.39}$, and there is no evidence of the transition that has been observed in this quantity in some recent work. We find that at high Reynolds numbers, $\chi$ and $a_0$ tend to values similar to those obtained by direct particle tracking measurements and by direct numerical simulation. However, at lower Reynolds number our estimates of $\chi$ and $a_0$ appear to be affected by the evaluation technique which imposes strict requirements on local homogeneity and isotropy.