$$f(t)=t^{3}+3t^{2}-12$$
$3t\left(t+2\right)$
$$3t^{3-1}+2\times 3t^{2-1}$$
$$3t^{2}+2\times 3t^{2-1}$$
$$3t^{2}+6t^{2-1}$$
$$3t^{2}+6t^{1}$$
$$3t^{2}+6t$$
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$t^{3}+3t^{2}-12$
