Your dy/dx is simply the slope of a Response vs. Amount (or concentration) plot, measured over the linear part of the plot.
Suppose you are using an HPLC with a UV detector.
If your signal (dy) is 0.1 absorbance units for an analyte injected at (dx) 0.05 mg/mL,
then sensitivity, S = dy/dx = 0.1/0.05 = 2 absorbance units per mg/mL.
Note that Sensitivity is not dimensionless, it always is stated as response per unit of sample.