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