Use the power rule along with "linearity":
f'(x)=2x^{-1/3}-2x and f''(x)=-2/3 x^{-4/3}-2.
The power rule says that d/dx(x^{n})=nx^{n-1} for any fixed number n. Linearity of the derivative operator says that d/dx(af(x)+bg(x))=af'(x)+bg'(x) for any fixed numbers a and b and any differentiable functions f and g.
Linearity can be extended, by using mathematical induction, to any finite "linear combination" of differentiable functions:
d/dx(a_{1}f_{1}(x)+a_{2}f_{2}(x)+\cdots+a_{n}f_{n}(x))=a_{1}f_{1}'(x)+a_{2}f_{2}'(x)+\cdots+a_{n}f_{n}'(x)
This can also be written using summation (sigma) notation as:
d/dx(\sum_{k=1}^{n}a_{k}f_{k}(x))=\sum_{k=1}^{n}a_{k}f_{k}'(x)
which can be thought of as a "distributive-like" property (even though the symbol d/dx is not a number that is being multiplied).
Furthermore, this is often extended to infinite series (sums), especially "power series", as long as x is within the interior of the "interval of convergence":
d/dx(\sum_{k=0}^{\infty}a_{k}(x-c)^{k})=\sum_{k=1}^{\infty}a_{k}k(x-c)^{k-1} (there's no typo here; the k=0 case on the right can be omitted)
