Hey guys. I'm having trouble with derivatives and I need someone's help with my homework. Could you guys please explain to me how to solve these problems?

1.

Given $\displaystyle y = f(x) = \frac{1}{x^2} - \sqrt[3]{x}$

Find the second derivative

$\displaystyle f"(x)=\frac{d^2y}{dx^2}$

2.

Given $\displaystyle f(x) = \frac{x^2}{1-3x}$

Find the derivative f'(x)

3.

Given $\displaystyle \Delta y = 2x^2(\Delta x+3x(\Delta x)^2-2(\Delta x)$

Find the derivative = $\displaystyle Lim \frac{f(x+\Delta x)-f(x)}{\Delta x}$

And I'm also stuck at this problem:

4.

Given $\displaystyle y=f(x)=2x^2-x$

Find $\displaystyle \Delta y=f(x+\Delta x)-f(x)$

Help is greatly appreciated.

Thanks guys!

--RS