Originally Posted by

**topsquark** $\displaystyle y = \left ( \frac{1 + \sqrt{x}}{x^{2/3}} \right ) ^3$

This is an exercise in the chain rule:

$\displaystyle y^{\prime} = \left [ 3 \left ( \frac{1 + \sqrt{x}}{x^{2/3}} \right )^2 \right ] \cdot \left [ \frac{\frac{1}{2 \sqrt{x}} \cdot x^{2/3} - (1 + \sqrt{x} ) \cdot \frac{2}{3}x^{-1/3} }{x^{4/3}} \right ] $

The first set of [ ] is the derivative of the "outer" function, the cube. The second set of [ ] is the derivative of the fraction inside the ( ). Of course, you still need to simplify this.

-Dan