# Confusion in derivation of Formula of divergence

This is from the book Mathematical Methods (Arfken), Can someone explain how did one del(x) and one dx came here,?

• what is del(x)? Anyway, its just standard formula $f(x+\Delta,y,z)-f(x,y,z)\approx \frac{\partial f}{\partial x}\Delta$, or are you confused about something else? Jun 15 at 5:33
• You mean on the RHS of the highlighted equation? Jun 15 at 5:38

What the LHS of the highlighted equation represents is the change in $$\rho v_x \,dy \,dz$$ between two $$x$$ values. Let the rate of change of this wrt $$x$$ be $$\frac{\partial (\rho v_x \,dy\, dz)}{\partial x}=\frac{\partial (\rho v_x )}{\partial x} dy\,dz$$
Now $$\Delta (\rho v_x)=\frac{\partial \rho v_x}{\partial x} \Delta x$$. $$\Delta x= x+dx/2-(x-dx/2)=dx$$, So the RHS becomes,
$$\Delta (\rho v_x)=\frac{\partial (\rho v_x )}{\partial x}\,dy \,dz \,dx$$