Physical Interpretation of adding the first derivative of a function to the original function

Question

Is it allowed to add a multiple of the first derivative of a function to its original peak function (say Gaussian/ exponentially modified Gaussian) to change its shape while maintaining the area underneath? I received this question from someone during a conference who said it is dimensionally inconsistent and does not have a physical meaning. I am not sure about its physical sense, but the reason for doing so is given below. Here is the background: Sometimes we can get two overlapping signals in chromatography as shown in the picture Under such conditions, we can add a small fraction of the first numerical derivative from the raw data. The peaks become sharper and if the resolution between the two peaks is decent, the area is also conserved because the area under the derivative is zero. What is the mathematical basis of this sharpening effect? It works to make the peaks appear more resolved. The expression could be written as Sharpened signal = Signal + (Constant)x first derivative. The constant is >0 and usually small (ranges from 0.001 to 5). Thanks.