$$(t^{2}+t-7)+(t^{3}+t^{2}+3t+4)$$
$t^{3}+2t^{2}+4t-3$
$$2t^{2}+t-7+t^{3}+3t+4$$
$$2t^{2}+4t-7+t^{3}+4$$
$$2t^{2}+4t-3+t^{3}$$
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$3t^{2}+4t+4$
$$\frac{\mathrm{d}}{\mathrm{d}t}(2t^{2}+t-7+t^{3}+3t+4)$$
$$\frac{\mathrm{d}}{\mathrm{d}t}(2t^{2}+4t-7+t^{3}+4)$$
$$\frac{\mathrm{d}}{\mathrm{d}t}(2t^{2}+4t-3+t^{3})$$
$$2\times 2t^{2-1}+4t^{1-1}+3t^{3-1}$$
$$4t^{2-1}+4t^{1-1}+3t^{3-1}$$
$$4t^{1}+4t^{1-1}+3t^{3-1}$$
$$4t^{1}+4t^{0}+3t^{3-1}$$
$$4t^{1}+4t^{0}+3t^{2}$$
$$4t+4t^{0}+3t^{2}$$
$$4t+4\times 1+3t^{2}$$
$$4t+4+3t^{2}$$
