Just use this tutorial:
http://www.mathhelpforum.com/math-he...-tutorial.html
Now to help you with your first problem:
$\displaystyle f(x) = x^3 - {x}^\frac {1}{3}$
From here, you will want to use the power rule so:
$\displaystyle f'(x) = 3x^2 - \frac {x}{3}^ {\frac {1}{3} - 1} = $$\displaystyle 3x^2 - \frac {x}{3}^ {\frac {-2}{3}}$
Now for the second you will need to use the chain rule and the product rule.
$\displaystyle f(x) = (s^2 + s + 1)^4 * (s-2)^7$
$\displaystyle f'(x) = (s^2 + s + 1)^4 * 7(s-2)^6 + (s-2)^7 * 8s(s^2 + s + 1)^3$