Answer:
[tex]-16\omega sin(\omega t + \pi/4)[/tex]
Explanation:
The function of the current with respect to time is the derivative of the charge function with respect to time t. We can apply chain rule to differentiate it:
[tex]I(t) = Q'(t) = (16cos(\omega t + \pi/4))' \\= -16(\omega t + \pi/4)' sin(\omega t + \pi/4) \\= -16\omega sin(\omega t + \pi/4)[/tex]
