Still playing catch up with my basic algebra so I've written out another question similar to one I'm doing for an assignment and it'd be great if anyone could have a look over it and see just how many errors I'm making.

$\displaystyle f(x) = 3x(1-x)s^4$

$\displaystyle \frac{df}{dx} = \frac{\lim}{\Delta x \rightarrow \infinity} = \frac{f(x+ \Delta x) - f(x)}{\Delta x}$

$\displaystyle 3(x + \Delta x) (1-(x + \Delta x))s^4 - 3x(1 - x) s^4 $

$\displaystyle 3x + 3 \Delta x +1 -x - \Delta x - 3x + 3x^2 $

$\displaystyle 3 \Delta x +1 -x - \Delta x - 3 \Delta x + 3x^2 $

* Can I cancel out the $\displaystyle s^4$ and $\displaystyle -s^4$ here or do they need to be multiplied (factored out?) with their respective brackets?

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

$\displaystyle \frac{3 \Delta x +1 -x - \Delta x +3x^2}{ \Delta x}$

$\displaystyle \frac{\lim}{\Delta x \rightarrow \infinity} = 1 - x + 3x^2$