Let $M$ be a regular surface and $F\in\mathfrak{X}(M)$ a non-uniform force field on $M$. The pressure is defined as: $$p=\frac{dF_A}{dA}\cdot \vec n$$ with $\vec n$ as normal vector of the surface.
What means by "derive the force respect to the total area $A$"?
Pardon me if I am not interpreting you right, but I think your question is "what does the expression $\frac{dF_A}{dA}$ mean?" Or "how do you differentiate Force with respect to Area?"
First, $A$ is area, but not the total area. Instead it refers to "unit area" - i.e., the area of an arbitrary region about the point of interest.
Second, $F_A$ is not $F$ itself, but is the total force applied across the arbitrary region.
So, for a given $p \in M$, $$\left.\frac{dF_A}{dA}\right|_p = \lim_{S \to p} \frac{\int_S F\,dA}{\int_S \,dA}$$ Where the limit is taken over regions $S$ containing $p$ and $S \to p$ means that the maximum distance from any point of $S$ to $p$ goes to $0$.