Flight Instructor with student reported a NMAC during departure with traffic overtaking them. Flight Instructor took evasive action to avoid a possible collision.

Narrative

It was a typical busy day at ZZZ with several aircraft departing and arriving into the airspace; along with multiple training aircraft in the pattern doing touch-and-goes. I was on an instrument training flight with my student. As we climbed out towards the south practice area passing roughly 1300 to 1400 feet; I briefly glanced at my EFB which was connected to my portable ADS-B in device and saw a target at our altitude nearly on top of our location. I immediately looked to my rear right and saw a Bonanza overtaking us with so little separation I instinctively took control and made a left turn to avoid conflict. I believe we were at a high risk of a collision if both of us continued on the same trajectory.I believe several things contributed to this loss of separation. Since it was a busy day in congested airspace; I should have been more aware of traffic departing after us in the same direction; especially faster moving traffic. The Bonanza should have maintained visual separation with us; given that we were both going to the Southeast. They made no attempt to alter their course and I believe were never aware of our presence. Because the Tower controller was so busy; I assume they were too busy to give a traffic callout to the overtaking Bonanza to make both of us aware of how close we were.While I am used to the fast-paced nature of ZZZ's Class D having trained and worked here; I have never had a loss of separation incident quite like this so I decided to report.Thank you for your consideration.