Originally Posted by

**JG89** I think I have seen one for the chain rule before (I may be wrong), if I did, then it was extremely messy. As for the quotient rule, if you let $\displaystyle h(x) = \frac{1}{g(x)} $ then $\displaystyle \frac{d^n}{dx^n} \frac{f(x)}{g(x)} = \frac{d^n}{dx^n} f(x) h(x) = \sum_{k=0}^{n}(_{n}C_{k})\frac{d^{n-k}}{dx^{n-k}}f\frac{d^k}{dx^k}h $

The reciprocal rule is just a special case of the quotient rule, where the function in the numerator is identically equal to 1, so the above formula covers that as well.