Answer
$A'(t)=\begin{bmatrix}
-3e^{-3t} & -2\sec^2t\tan t\\
6t^2 & -\sin t\\
\frac{6}{t} & -5
\end{bmatrix} $
Work Step by Step
$A'(t)$ is the derivative of the matrix $A(t)$
$A'(t)=\begin{bmatrix}
-3e^{-3t} & -2\sec^2t\tan t\\
6t^2 & -\sin t\\
\frac{6}{t} & -5
\end{bmatrix} $
