Lastly, we have to differentiate quotients.
Think of this example, . In such a case it is no use to try to work out the division beforehand, because will not divide into , neither have they any common factor. So there is nothing for it but to go back to first principles, and find a rule.
So we will put ;
where and are two different functions of the independent variable . Then, when becomes , will become ; and will become ; and will become . So then
.
Now perform the algebraic division, thus:
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