$$(3u^{2}-3u+6)+(-u^{2}+4u+3)$$
$2u^{2}+u+9$
$$3u^{2}+u+6-u^{2}+3$$
$$3u^{2}+u+9-u^{2}$$
$$2u^{2}+u+9$$
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$4u+1$
$$\frac{\mathrm{d}}{\mathrm{d}u}(3u^{2}+u+6-u^{2}+3)$$
$$\frac{\mathrm{d}}{\mathrm{d}u}(3u^{2}+u+9-u^{2})$$
$$\frac{\mathrm{d}}{\mathrm{d}u}(2u^{2}+u+9)$$
$$2\times 2u^{2-1}+u^{1-1}$$
$$4u^{2-1}+u^{1-1}$$
$$4u^{1}+u^{1-1}$$
$$4u^{1}+u^{0}$$
$$4u+u^{0}$$
$$4u+1$$
