Question

Regarding differentiating... Is it always possible to rearrange a quotient into a product and apply the product rule?

Answer 1

usually you can be simply doing the quotient rule is much easier in most cases

Answer 2

*but

Answer 3

ya, its always possible,
but if you do so, sometimes it becomes too lenthy ;)

Answer 4

if it comes to differentiate 1/x^2 you can write it as, (x)^-2

Answer 5

i'm aware of how to re-arrange functions, I was just curious to know if there is ever a case where we cannot use the product rule on a quotient

Answer 6

no because you prove it via the product rule
it is always the case that \(\frac{f}{g}=f\times \frac{1}{g}\) but why you would want to work with \(\frac{1}{g}\) is not always clear