$$(z^{2}+2-7)+(z^{3}+z^{2}+3z+6)$$
$z^{3}+2z^{2}+3z+1$
$$z^{2}-5+z^{3}+z^{2}+3z+6$$
$$2z^{2}-5+z^{3}+3z+6$$
$$2z^{2}+1+z^{3}+3z$$
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$3z^{2}+4z+3$
$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{2}-5+z^{3}+z^{2}+3z+6)$$
$$\frac{\mathrm{d}}{\mathrm{d}z}(2z^{2}-5+z^{3}+3z+6)$$
$$\frac{\mathrm{d}}{\mathrm{d}z}(2z^{2}+1+z^{3}+3z)$$
$$2\times 2z^{2-1}+3z^{3-1}+3z^{1-1}$$
$$4z^{2-1}+3z^{3-1}+3z^{1-1}$$
$$4z^{1}+3z^{3-1}+3z^{1-1}$$
$$4z^{1}+3z^{2}+3z^{1-1}$$
$$4z^{1}+3z^{2}+3z^{0}$$
$$4z+3z^{2}+3z^{0}$$
$$4z+3z^{2}+3\times 1$$
$$4z+3z^{2}+3$$
