A new method of the Quench Detection Systems (QDS) designed for the LHC 600 A corrector magnet circuits and 6 kA Individual Powered Quadrupole (IPQ) magnet circuits is presented. In order to improve the dependability of QDS a direct measurement of the power converter current derivative is proposed. Actually, the quench detection scheme for the 600 A corrector magnet circuits uses the current derivative numerically evaluated from a direct current measurement. In order to make the calculation of the derivative stable, the input signal is heavily filtered, thus introducing a significant phase shift, which restricts the operational range of circuit parameters like ramp rate and acceleration. For the 6 kA IPQ magnet circuits the main quench detection is based on a classical bridge configuration. The introduction of an additional detection channel for the direct measurement of the current derivative helps to overcome the lack of sensitivity to fully aperture symmetric quenches of the bridge configuration. Transformer-based current derivative sensors are currently under development, using cut-cores for easy prototyping, performance control and installation. Prototypes for the ±600 A current range and ramp rates between 0.1 and 5 A/s were build using different core materials (electrical steel and nanocrystalline cores), and pickup coils with 10000 and 20000 windings. In order to characterize the prototypes, the performance was defined in terms of mean sensitivity of the sensor response in V/A/s and the Performance Quality Factor (PQF), defined as a percentage of nonlinearity of the response. An optimization procedure was implemented for finding the best configuration of the sensors, i.e. the airgap in the cut core in order to maximize the mean sensitivity and to minimize the PQF. The tests were carried out at different working points (current ranges and rates) showing promising results (PQF < 0.5 % with a sensitivity of 5.5 mV/A/s).