# Math Help - quotient rule for higher order derivatives

1. ## quotient rule for higher order derivatives

what is quotient rule for higher order derivatives ? i mean the one analogous to leibniz rule .

2. Originally Posted by mmzaj
what is quotient rule for higher order derivatives ? i mean the one analogous to leibniz rule .
If you consider that:

$\frac{d}{dx} \bigg(\frac{f(x)}{g(x)}\bigg) = \frac{d}{dx} \bigg(f(x) \times \frac{1}{g(x)}\bigg) = \frac{d}{dx}\bigg( f(x) \times h(x)\bigg)$ where $h(x) = \frac{1}{g(x)}$, then the generalised product rule holds.

The quotient rule is simply a by-product of the product rule, and one of the most familiar proofs of the quotient rule is based entirely on the product rule.

3. but then you gotta use the reciprocal rule for the nth derivative , with isn't easier from finding a generalization for the quotient rule !!