Since W_o = 10^-12 W/m², and using the logarithm law for the log of a fraction, we can write:

Now, using the formula for the derivative of a logarithm, and because log 10^-12 is a constant, we have:

Now we substitute our given values for W and dW/dt from the question:

The units are dB/s since the sound pressure (in dB) is changing over time.