differentiate: s^1/3 - 1 / s^2/3 -1

(1/3) s^-2/3 + (2/3) s^(-5/3)

shouldn't you apply quotient rule rather than product rule? and for that matter, wouldn't the last bit be s^-1/3

1/s^2/3 = s^(-2/3)

-2/3-1 = -5/3

oh okay. but what about the rule? it should be quotient.

it doesnt matter. it is easier my way

I know, I tried that too. but then that's not the answer :/ somehow the answer is 1/3 (s^1/3 +1)^-2 s^-2/3

wait. the question is ambiguous. can you post your question using the equation button below?

type in frac{1}{s} to get 1/s

\[g(s) = s ^{1/3} - 1 \div s ^{2/3} -1\]

does that make it clear?

do you mean\[g(s)=s ^{\frac{1}{3}} - \frac{1}{s ^{\frac{2}{3}}-1}\]

no, the whole numerator divided by the denominator

oh so it is\[\frac {s ^{\frac{1}{3}}-1}{s ^{\frac{2}{3}}-1}\]

correct?

in that case you should use the quotient rule

yessss! so can you tell me the answer..

i got \[\frac{-1-s ^{\frac{2}{3}}+2s ^{\frac{1}{3}}}{3s ^{\frac{2}{3}} (s ^{\frac{2}{3}}-1)^{2}}\]

how did you get it? explain please..

I just used the quotient rule and simplified.