Does slew rate depend on frequency of input signal?
In an op-amp, the slew rate is defined as the rate at wich the output voltage changes, for a step change at the input, with respect to time.

If you apply a step at the input, you obtain a ramp on the output, and the output voltage is changing at the maximum possible speed for that particular op-amp. So the slew rate represents the maximum slope in the V/T curve that you can obtain on the output.

If you are amplifying a sinusoid, the maximum slope that you encounter is at zero crossing, and its vaule is

$$\text2\pi \times f \times V_m$$

You cannot obtain a sinusoid on the output if that slope is greater than the op-amp slew rate.

The slew rate is not a characteristic of the waveform, but of the amplifier.

Since the slope of the sinusoid depends on the frequency AND the amplitude, the selw rate affects more larger signals than small ones.

Smaller signals are more affected by the gain-bandwidth product.