$$4x^{3}-x^{2}-x-2; x^{5}+2x^{2}$$
$4x^{3}+x^{2}-x-8$
$$4x^{3}-x^{2}-x-8+2x^{2}$$
$$4x^{3}+x^{2}-x-8$$
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$12x^{2}+2x-1$
$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}-x^{2}-x-8+2x^{2})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}+x^{2}-x-8)$$
$$3\times 4x^{3-1}+2x^{2-1}-x^{1-1}$$
$$12x^{3-1}+2x^{2-1}-x^{1-1}$$
$$12x^{2}+2x^{2-1}-x^{1-1}$$
$$12x^{2}+2x^{1}-x^{1-1}$$
$$12x^{2}+2x^{1}-x^{0}$$
$$12x^{2}+2x-x^{0}$$
$$12x^{2}+2x-1$$
