Let

$$A(t) = \left\lbrack \begin{array}{cc} 2 & \ln\!\left(\left|t\right|\right) \\ \sqrt{4-t} & e^{5t} \end{array} \right\rbrack.$$

1. Find $A'(t)$.

   $A'(t) =$

   $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

   
   
   
2. Find $A''(t)$.

   $A''(t) =$

   $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

   
   
   
3. $A(t)$ is defined for all $t$ in the interval(s) help (intervals)
   
   $A'(t)$ is defined for all $t$ in the interval(s) help (intervals)
   
   $A''(t)$ is defined for all $t$ in the interval(s) help (intervals)