The graph of `W = cos 0.2t` is as follows:

decibels graph

The graph of

`P=10\ log {:(cos\ 0.2t)/(10^(-12)):}`

is given by:

decibels graph

We see that the slope is negative, so we expect a negative answer.

Since

`P=10\ log {:(cos\ 0.2t)/(10^(-12)):}`

we have:

`(dP)/(dt) = d/(dt)10\ log_10 (cos\ 0.2t)/(10^(-12))`

`=10[1/W log_10e](dW)/(dt)`

`=10[1/(cos\ 0.2t)\ log_10e]xx` `(-0.2\ sin\ 0.2t)`

`=-0.869\ tan\ 0.2t`

At `t = 1\ "s"`, the value of the derivative is `-0.176\ "dB/s"`. (Of course, t is in radians).

Our answer is negative, as expected.

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