# Confusion in property of Z transform of ideal sampled waveform

I was reading about z transfom of ideal sampled signals and one of the properties of Z transform of sampled signal that surprised me,here it is (image)

So here this property of Z transform is quite unusual compare to the property we use for discrete time signals (there we differentiate with respect to z) .

How this property can be proved mathematically (even a hint ) and why its not differentiated with respect to z as we generally do