**The Quotient Rule**

This approach to the quotient rule is credited to Maria Gaetana Agnesi (1718 – 1799) who wrote the first known mathematics textbook *Analytical Institutions *(1748) to help her brothers learn algebra.

The quotient rule can also be proven from the definition of derivative. But here is a simpler approach – as a corollary of the product rule.

Begin by letting .

Then

and .

Then solving for :

**Mnemonics **

I’m not really one for mnemonics. I cannot spell SOHCOHTOA without saying to myself, “sine, opposite over hypotenuse; cosine, adjacent …” It seems better to me anyway to have student just memorize the formulas in words using the correct terms:

*The derivative of a product is the first factor times the derivative of the second plus the second factor times the derivative of the first. *

*The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all divided by the square of the denominator. *

But whatever works for you. *Lo Di Hi*

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