# Infinitesimal volume using differentials

girolamo
Hi, I don't understand why in some texts they put that infinitesimal volume dV = dx dy dz. If V = x y z, infinitesimal volume should be dV = y z dx + x z dy + x y dz, by partial differentiation. Thanks

Mentor
Hi, I don't understand why in some texts they put that infinitesimal volume dV = dx dy dz.
Because the dimensions of the box are dx, dy, and dz. The volume of this box is dV, which is dx * dy * dz.
If V = x y z, infinitesimal volume should be dV = y z dx + x z dy + x y dz, by partial differentiation. Thanks

This would be the change in volume of a box whose dimensions are x, y, and z, and whose dimensions change by dx, dy, and dz.

Staff Emeritus