Electrical Engineering (Signal Degradation & Attenuation)

An electrical engineer is analyzing high-frequency AC signal loss across a subsea telecommunications cable subject to inductive noise and dielectric dissipation. The measured output voltage signal $V(t)$ (in Volts) over time $t$ (in milliseconds) follows a multi-factor decaying wave:

1. Apply the natural logarithm to both sides of the voltage expression and expand completely using logarithmic product, quotient, and power properties.
2. Differentiate implicitly with respect to $t$ to find an expression for the instantaneous rate of voltage change $\frac{dV}{dt}$.
3. Evaluate the exact rate of voltage degradation $\frac{dV}{dt}$ at $t = 2\text{ ms}$, given that the carrier voltage amplitude at that instant is $V(2) \approx 0.0104\text{ V}$.