6. $(x+h{)}^4=x^4+4h{x}^3+6h^2{x}^2+4h^{3}x+h^4$.

7. The gradient is $4x^3$.

9.

(i) $4x$;
(ii) $34x$;
(iii) $-2x$;
(iv) $2ax$;
(v) $6x^2$;
(vi) $3a{x}^2$;
(vii) $na{x}^{n-1}$.

10. You should see that you get the gradient of $y=x^3$ plus the gradient of $y=x^2$. Similarly, the gradient of $y=x^n+x^m$ is just the gradient of $y=x^n$ plus the gradient of $y=x^m$, that is, $n{x}^{n-1}+m{x}^{m-1}$.