Discussion
What limits a differential pair's slew rate?
Answer: C
When the input difference is large enough, all the tail current is steered to one side, and that fixed current is all there is to charge whatever capacitance follows - so the output cannot change faster than the current divided by the capacitance. Transition frequency and load resistance govern the small-signal response instead, and common-mode range is unrelated. A large-signal limit set by a fixed current is quite separate from the small-signal bandwidth, and an amplifier can be fast by one measure and slow by the other.
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