The tent space theory, which was established by Coifman, Mayer and Stein in 1985, is an effective tool for studying operators from Hardy spaces H^p to Lebesgue spaces L^q for 0<q<p<∞. In this talk, by applying the tent space theory, we completely characterize the boundedness and compactness of derivative area operators, which are compositions of area operators and differentiation operators, from H^p on the unit ball B_n into L^q (S_n ) for 0<p,q<∞. As byproducts, we also give complete characterizations for a positive Borel measure μ such that R^k: H^p→L^q (μ) is bounded or compact on the unit ball B_n for all 0<p,q<∞ in terms of Carleson measures and tent spaces, where R^k (k∈N) is the radial derivative of order k. This is a joint work with Xiaosong Liu, Zengjian Lou, and Zixing Yuan.