I am given the following set of equations from a physics course, which is about longitudinal waves in rods.
My questions are:
On the second line you have $ (\frac{\partial \Delta}{\partial x})dx $ If you are already specifying you are doing a partial differentiation with respect to the x-direction. Why do you need to specify it a second time by adding $dx$?
interpretation of $ (\frac{\partial \Delta}{\partial x})dx $: "the rate of change of the change of pressure in the x-direction" Could someone confirm me this is a correct interpretation? This sounds quite odd to me
what's the difference between those notations: $\frac{\Delta l}{l} $ and $\frac{\partial D}{\partial x}$ . The difference confuses me what is the actual difference?