$$2 p ^ { 3 } - 3 p ^ { 2 } + 4 p - 5 - 6 p ^ { 3 } + 2 p ^ { 2 } - 8 p - 2 + 6 p + 8$$
$1+2p-p^{2}-4p^{3}$
$$-4p^{3}-3p^{2}+4p-5+2p^{2}-8p-2+6p+8$$
$$-4p^{3}-p^{2}+4p-5-8p-2+6p+8$$
$$-4p^{3}-p^{2}-4p-5-2+6p+8$$
$$-4p^{3}-p^{2}-4p-7+6p+8$$
$$-4p^{3}-p^{2}+2p-7+8$$
$$-4p^{3}-p^{2}+2p+1$$
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$2-2p-12p^{2}$
$$\frac{\mathrm{d}}{\mathrm{d}p}(-4p^{3}-3p^{2}+4p-5+2p^{2}-8p-2+6p+8)$$
$$\frac{\mathrm{d}}{\mathrm{d}p}(-4p^{3}-p^{2}+4p-5-8p-2+6p+8)$$
$$\frac{\mathrm{d}}{\mathrm{d}p}(-4p^{3}-p^{2}-4p-5-2+6p+8)$$
$$\frac{\mathrm{d}}{\mathrm{d}p}(-4p^{3}-p^{2}-4p-7+6p+8)$$
$$\frac{\mathrm{d}}{\mathrm{d}p}(-4p^{3}-p^{2}+2p-7+8)$$
$$\frac{\mathrm{d}}{\mathrm{d}p}(-4p^{3}-p^{2}+2p+1)$$
$$3\left(-4\right)p^{3-1}+2\left(-1\right)p^{2-1}+2p^{1-1}$$
$$-12p^{3-1}+2\left(-1\right)p^{2-1}+2p^{1-1}$$
$$-12p^{2}+2\left(-1\right)p^{2-1}+2p^{1-1}$$
$$-12p^{2}-2p^{2-1}+2p^{1-1}$$
$$-12p^{2}-2p^{1}+2p^{1-1}$$
$$-12p^{2}-2p^{1}+2p^{0}$$
$$-12p^{2}-2p+2p^{0}$$
$$-12p^{2}-2p+2\times 1$$
$$-12p^{2}-2p+2$$
