Let $A(t)$ be a differentiable matrix-valued function defined by: $A(t) = \begin{pmatrix} e^t & t & 1 \\ 1 & e^{2t} & t^2 \\ t & 1 & e^{3t} \end{pmatrix}$ Find the derivative of the determinant of $A(t)$ with respect to $t$ evaluated at $t = 0$.