Question

Find the derivative...

Answer 1

\[x \div \sqrt[3]{x ^{3}-1}\]

Answer 2

use the quotient rule to do this

dy/dx =( vdu - udv ) / v^2
-- --
dx dx

= [ (x^3 -1))^(1/3) * 1 - x* 3x^2 * 1/3 (x^3 - 1)^(-2/3)] / (x^3 -1)^(2/3)

the rest is algebra - a bit messy though

Answer 3

ok - ill simplify what i've got on paper -easier that way

Answer 4

denominator squared would be (x^3-1)^(1/9) right?

Answer 5

no denominator squared - (x^3-1)^ (2/3) - the exponents are added

Answer 6

the algebra is horrible with this one - maybe it would be better writing it as
x* (x^3-1)^ (-1/3) and use the product rule

Answer 7

okay, I'll try that

Answer 8

- and i'm tired ( late here in uk) !!

Answer 9

thanks

Answer 10

i've got the answer by using product rule
its -1 / (x^3 - 1) ^(4/3)

Answer 11

it checked out with wolfram so it is correct

Answer 12

Thanks for your help

Answer 13

ok - thats what you have to aim for - use product rule