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find the derivative of (x^2+1) 3rd root of x^2+2

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If you mean (x^2+1) * (x^2+2)^(1/3) then just use the product rule and chain rule.

y = u*v^n
y' = u'v^n + u*n*v^(n-1)*v'

u = x^2 + 1
u' = 2x

v = x^2 + 2
v' = 2x

y' = 2x*cbrt(x^2+2) + 2x*(x^2+1)* 1/3 * (x^2 + 2)^(-2/3)

Feel free to simplify further. You're doing calculus; algebra should be a breeze.
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