This question already has an answer here:
When we started the study of kinematics we defined position and its change with respect to time. After that we defined time derivative of velocity which gave us acceleration.
These 3 concepts really helped us and we extended our study from kinematics to dynamics which provided us a simple relation between acceleration and force.
If we would have defined the time derivative of acceleration then what would we have got? What would have been its physical significance? How it would have helped us in study of dynamics?
I want to conclude my question by just asking that why don't we define the time derivative of acceleration?