A conducting coil, with current $i(t)=5\mathrm{.}40e^{-0\mathrm{.}0250t}sin(120t),$ with $i$ in amperes and $t$ in seconds, is placed next to a second coil, end to end. At $t=0\mathrm{.}840s,$ a lab tech measures the emf across the second coil, and the result is $-3\mathrm{.}90$ V $.$ What is the mutual inductance $($in mH $)$ of the coils?

Apply the equation for mutual inductance. You will need to take the derivative of the current function. mH