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A CD4049 also does not have enough output current to quickly switch a Mosfet.
A Mosfet has a high gate-source capacitance plus dynamic capacitance from the drain to the gate. For the Mosfet to switch quickly (so it stays cool) then it needs gate pulses with fairly high current to quickly charge and discharge the capacitance.
You can see the capacitance on the datasheet for your Mosfet, decide how quickly you want it to switch then calculate the required transistor driver current.
