On the Differentiation of Functions of Two or More Variables

Abstract

If two or more variable quantities x, y, z are independent of each other, it can happen that while one of the variables increases or decreases, the other variables remain constant. Since we have supposed that there is no connection between the variables, a change in one does not affect the others. Neither do the differentials of the quantities y and z depend on the differential of x, with the result that when x is increased by its differential dx, the quantities y and z can either remain the same, or they can change in any desired way. Hence, if the differential of x is dx, the differentials of the remaining quantities, dy and dz, remain indeterminate and by our arbitrary choice will be presumed to be either practically nothing or infinitely small when compared to dx.