Differentiation was ok - but you should now

*simplify*.

Differentiation is not ok. Where on earth did you get that factor $\displaystyle 4x^2-3$? The second factor was $\displaystyle (3x^2-5x-3)$, no?

And, again, you need to simplify.

Almost, but not quite: everything seems ok except the term $\displaystyle 5x^{5/3}$. Think about it. Did you apply the power rule correctly? I don't think so.

Looks ok to me, but maybe one would want to ask whether some simplification is possible. Well, maybe - or maybe not.

Differentiation seems ok, but what about simplifying the whole mess? After all one might be able to collect same powers of x. $\displaystyle y$ is a polynomial of degree 6, therefore $\displaystyle y'$ must be a polynomial of degree $\displaystyle 6-1=5$. I think it should be possible to make a polynomial of degree 5 look a little tidier on the page than this...

Differentiation seems ok to me. (I'm a little surprised to see you put the "inner derivative" $\displaystyle 21x^2-10x+6$ as the second factor here.) I don't think one would want to try to "simplify" here by multiplying out

No, for some reason you have botched this one up completely. What about

$\displaystyle y'=5(4x^2+3)^4\cdot 8x\cdot (2x^2-1)^4+(4x^2+3)^5\cdot 4(2x^2-1)^3\cdot 4x$

Now here, you would simplify by factoring out $\displaystyle (4x^2+3)^4\cdot (2x^2-1)^3$

Judging from the above, you should be able to differentiate this one as well.