what is quotient rule for higher order derivatives ? i mean the one analogous to leibniz rule .
what is quotient rule for higher order derivatives ? i mean the one analogous to leibniz rule .
If you consider that:
$\displaystyle \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 $\displaystyle 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.