Input Stage Degeneration
Let's improve the slew rate of our amplifier. I have increased the Long Tailed Pair (LTP) emitter resistors to 487R. This increases the total emitter-to-emitter resistance to 1k, reducing its transconductance. To have a negative feedback gain crossover frequency fc at 500kHz, C1 must be reduced: C1 = 1/(2*Pi*fc*Rltp*Acl). Rltp is the emitter-to-emitter resistance of our Long Tailed Pair, Acl is the closed loop gain of our amplifier, about 20, so C1 = 15.915pF. As we are using a current mirror load, "The use of both signal currents from the collectors of the LTP effectively doubles the transconductance of the LTP. This means that C1 must be doubled". Let's round the answer up to the nearest E24 preferred value, 33pF. There is a maximum ±2mA (half the tail current) available from the input stage to charge and discharge C1, this results in an achievable slew rate of 2mA/33pF = 60.606V/us. Also, "the input stage has been made significantly more linear by the addition of the emitter degeneration. This leads to lower input stage distortion under virtually all signal conditions" (from Designing Audio Power Amplifiers, Bob Cordell, ISBN: 978-0-07-164025-1).