Find the derivative of the vector function
$\mathbf r(t) = t\mathbf a \times (\mathbf b + t\mathbf c)$, where
$\mathbf a = \langle 5, 2, 1\rangle$, $\mathbf b = \langle 3, 4, 3\rangle$, and $\mathbf c = \langle -1, 1, -3\rangle$.
$\mathbf r'(t) = \langle$ , , $\rangle$

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