$$(5x+5)+(2x+7)$$
$7x+12$
$$7x+5+7$$
$$7x+12$$
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$7$
$$\frac{\mathrm{d}}{\mathrm{d}x}(7x+5+7)$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(7x+12)$$
$$7x^{1-1}$$
$$7x^{0}$$
$$7\times 1$$
$$7$$