We have studied high derivative thermoelastic properties such as the pressure derivatives of bulk modulus and the volume dependence of the Gruneisen parameter in case of MgO for a wide range of pressures down to compression V/V0 = 0.6, and temperatures up to 3,000 K approaching the melting temperature. We have used the isothermal pressure–volume equation of state (EOS) based on the adapted polynomial expansion of second order (AP2) due to Holzapfel. The results for the P–V–T relationships and high derivative properties have been obtained using the Holzapfel AP2 EOS. The pressure derivatives of bulk modulus and volume derivatives of the Gruneisen parameter have been determined using the free volume theory. A relationship between the pressure derivative of bulk modulus and the ratio of pressure and bulk modulus has been found to hold good.