Question

differentiate using quotient rule:
s^1/3 - 1 / s^2/3 - 1

Answer 1

I presume you mean \[(s^(1\div3)-1)\div(s^(2\div3)-1)\]

sorry, this looks a bit messy. In words "(cube root of s, minus1) on top line, (cube root of s all squared, minus 1) on the bottom line"

If so, bottom line is a difference of two squares, so simplify forst before differentiating

Answer 2

how is the bottom line the difference of two squares?

Answer 3

do you mean (s^1/3)^2 - (1)^2

Answer 4

Difference of two squares is like a^2 - b^2

In this case a = s^(1/3) and b = 1, so

bottom line is (S^(1/3) -1)(s^(1/3) + 1)

then cancel top and bottom factors to get a much easier expression to differentiate.

Answer 5

oh yeah.. that made it a lot easier. thanks! :)