Exactly what I said. Given the same voltage swing, bandwidh and slew rate are directly related.
Sorry, but no, bandwidth has nothing to do with slew rate.
Slew rate is how fast the output voltage can swing, but this tells you nothing about the frequency of the signal doing the swinging. For example, an amp with a slew rate of 1V/us could theroetically swing 8Vpk at 20kHz, or 1.6Vpk at 100kHz. So does that mean its bandwidth ios 20kHz, or 100kHz? Neither. It tells you nothing about the bandwidth.
Slew rate comes from an amplifiers ability to dump current into a capacitor. It can be defined as:
Slew rate = Ipk/Capacitance
So why do audio power amps claim a slew rate? Where is the capacitor?
It is inside the amplifier. The slew rate is determined by the input circuit's ability to dump current into the Miller capacitance of the next amplifying stage.
Bandwidth is an entirely separate issue. The bandwidth of an amplifier is the same whether yopu're talking about small signals or large ones. Ideally you want the slew rate to be high enough that when amplfying the highest frequency
at the highest amplitude, you don't get slew limiting distortion. But if the slew rate is too small, you could hit slew limiting even at frequencies well within the bandwidth, simply because you're asking the amplifier to produce signal swings that are too big. Back off the signal swing, and you move away from slew limiting.