$
\eqalign{
& f(x) = - \frac{1}
{{3x^{2} }} = - \frac{1}
{3}x^{ - 2} \to f'(x) = - \frac{1}
{3} \cdot - 2 \cdot x^{ - 3} = \frac{2}
{{3x^{3} }} \cr
& g(x) = 2 - \frac{1}
{{\left( {3x} \right)^{3} }} = 2 - \left( {3x} \right)^{ - 3} \to g'(x) = - - 3 \cdot \left( {3x} \right)^{ - 4} \cdot 3 = \frac{9}
{{\left( {3x} \right)^{4} }} \cr
& of\,\,beter: \cr
& g(x) = 2 - \frac{1}
{{\left( {3x} \right)^{3} }} = 2 - \frac{1}
{{27}}x^{ - 3} \to g'(x) = - \frac{1}
{{27}} \cdot - 3x^{ - 4} = \frac{1}
{{9x^4 }} \cr}
$
En nog zo iets....
$
\eqalign{
& y = \frac{{x^{2} }}
{{\root 3 \of x }} = \frac{{x^{2}}}
{{x^{\frac{1}
{3}} }} = x^{2} \cdot x^{ - \frac{1}
{3}} = x^{1\frac{2}
{3}} = x^{\frac{5}
{3}} \cr
& y' = \frac{5}
{3}x^{\frac{2}
{3}} = \frac{5}
{3}\root 3 \of {x^{2}} \cr}
$