Now we know that we may neglect small quantities of the second and third orders; since, when and are both made indefinitely small, and will become indefinitely smaller by comparison. So, regarding them as negligible, we have left:
.
But ; and, subtracting this, we have:
,
and
.
Case 3.
Try differentiating . Starting as before by letting both and grow a bit, we have:
.
Working out the raising to the fourth power, we get
.
Then striking out the terms containing all the higher powers of , as being negligible by comparison, we have