$$\frac{d}{dx}[[6x^{-6}+3x^{2}+2x+1]]$$
$6x+2-\frac{36}{x^{7}}$
$$-6\times 6x^{-6-1}+2\times 3x^{2-1}+2x^{1-1}$$
$$-36x^{-6-1}+2\times 3x^{2-1}+2x^{1-1}$$
$$-36x^{-7}+2\times 3x^{2-1}+2x^{1-1}$$
$$-36x^{-7}+6x^{2-1}+2x^{1-1}$$
$$-36x^{-7}+6x^{1}+2x^{1-1}$$
$$-36x^{-7}+6x^{1}+2x^{0}$$
$$-36x^{-7}+6x+2x^{0}$$
$$-36x^{-7}+6x+2\times 1$$
$$-36x^{-7}+6x+2$$
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$6+\frac{252}{x^{8}}$
