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Here, I'll try to reconstruct the derivation and try to point out the parts where it confused me.

First suppose we have a fluid with definite volume where its density is the same throughout, hence it's uniform. Now, if we take an element fluid with thickness dy then and its top and bottom surfaces are the same, say A. Its volume is dV=A*dy, it's mass dm=(rho)*dV=(rho)*A*dy, and its weight w is dmg=(rho)*g*A*dy.

Where rho is the density of the fluid.

When the book gave an analysis of the forces on the y-component of that certain element fluid, the upward force is given by F(upward) = pA. I understand that part since there is pressure (p) pressing the fluid at its bottom area. Now, when the book gave the downward forces, it's given by F(downward) = (p+dp)*A and this confused me, where did the additional dp come from? There is the p that presses the upper area of the fluid but what about dp? Also the other downward force is the weight, but the fluid is in equilibrium, so:

(Sum)Fy = pA-(p+dp)*A-W=0 *The fact that there is force p*A upward and downward plus the weight is also non intuitive for me.*

So yeah, the biggest question for me is dp in the derivation, what is that?