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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