Originally Posted by

**ixo** I'm trying to solve a quotient problem but apparently my radical exponent algebra is rusty. Can someone tell me if this is right?

use quotent rule to differentiate the function:

(x^(1/3))/(x^3+1)

I've used the rule to get:

(x^3+1) 1/3 x^(-2/3) - x^(1/3) (3x^2) / (x^3+1)^2

My problem is the 1/3 x^(-2/3) - x^(1/3) (3x^2) (I'll plug this back in)

I transform into 1/3x^(**-**2/3) - (x^(1/3) (3x^2) (3x^(2/3))) / 3x^(2/3)

then 1- (x^(1/3) (3x^(2/1)) (3x^(2/3))) / 3x^(2/3)

then 1 - (x^(1/3)9x^(8/3)) / 3x^(2/3)

then 1 - 9x^3 / 3x^(2/3)

plug back in to get: x^3 +1 - 9x^3 / 3x^(2/3) (x^3+1)^2

then**(** 1-8 x^3 **)**/**(** 3x^(2/3) (x^3+1)^2**)**

That is the correct answer but i just want to make sure i am using the radical multiplication rule correctly.

Thanks.

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