okay i messed that up okay!. Gone through it again i will add my workings this time.

So

1) C - correct , simple $\displaystyle 7(x)^3 $ becomes $\displaystyle 21x^2 $then$\displaystyle -4sin(x)$ becomes $\displaystyle -4cos(x) + 5/x $ as loge(x) becomes 5/x.

2) okay so if y= uv then $\displaystyle dy/dx = u dv/dx + v du/dx $

so $\displaystyle u = x^4$ and $\displaystyle v = log_e(x)$

then $\displaystyle du/dx = 4x^3 $

and $\displaystyle dv/dx = 1/x $

so it becomes $\displaystyle dy/dx = x^4 . 1/x + log_e(x) . 4x^3$

this then becomes

$\displaystyle 4x^3log_e(x) + x^4 $

so B?

Not quite...what's $\displaystyle x^4\cdot\frac{1}{x}$??
3) the quotient rule states $\displaystyle dy/dx = (v du/dx - u dv/dx)/v^2$

so then $\displaystyle v = x^2+1 and u = x^2-1 $

and $\displaystyle dv/dx = 2x $

$\displaystyle du/dx = 2x $

so then it becomes $\displaystyle (x^2+1.2x - x^2-1.2x)/(x^2+1)^2$

thus $\displaystyle 4x/ ( x^2 + 1) ^ 2 $

so B?

Correct!
4) Chain rule!!

my bad so $\displaystyle y = log_e(x^3+3x)$

then $\displaystyle u = (x^3 + 3x)$$\displaystyle so log_e(u) = 1/u.du/dx$ then

$\displaystyle 1/(x^3 + 3x) . 3x^2 + 3 $so becomes

$\displaystyle 3(x^2+1)/x^3+3x$

so c?

Correct!
i'll write the rest whilst i wait for a reply!. Thankyou it has really helped! I'm awful at maths.