An Introduction to Differentiation
4. $(x+h)^3=x^3+3h x^2+3h^2 x+h^3$.
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) $34 x$;
(iii) $-2x$;
(iv) $2a x$;
(v) $6x^2$;
(vi) $3a x^2$;
(vii) $n a x^{n-1}$
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,
$n x^{n-1}+m x^{m-1}$.