Neglecting the small quantities of higher orders, this becomes
.
Subtract the original , and we have left:
.
.
So the has quite disappeared. It added nothing to the growth of , and does not enter into the differential coefficient. If we had put , or , or any other number, instead of , it would have disappeared. So if we take the letter , or , or to represent any constant, it will simply disappear when we differentiate.
If the additional constant had been of negative value, such as or , it would equally have disappeared.
Multiplied Constants.
Take as a simple experiment this case:
Let .
Then on proceeding as before we get:
.
Then, subtracting the original , and neglecting the last term, we have