posted by vicki .
find the derivative of (x^2+1) 3rd root of x^2+2
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.