  A massive multiple input multiple-output system is very important to optimize
the trade-off energy efficiency and spectral efficiency in fifth-generation
cellular networks. The challenges for the next generation depend on increasing
the high data traffic in the wireless communication system for both EE and SE.
In this paper, the trade off energy efficiency and spectral efficiency based on
the first derivative of transmit antennas and transmit power in a downlink
massive MIMO system has been investigated. The trade off EE-SE by using a
multiobjective optimization problem to decrease transmit power has been
analyzed. The EE and SE based on constraint maximum transmit power allocation
and a number of antennas by computing the first derivative of transmit power to
maximize the trade-off energy efficiency and spectral efficiency has been
improved. From the simulation results, the optimum trade-off between EE and SE
can be obtained based on the first derivative by selecting the optimal antennas
with a low cost of transmit power. Therefore, based on an optimal optimization
problem is flexible to make trade-offs between EE-SE for distinct preferences
