Using chain rule, we have:

`(dP_a)/(dt)=(dP_a)/(d theta)(d theta)/(dt)`

Now `P_a= P\ sec\ θ = 12\ sec\ θ` (since `P = 12\ "W"`)

`(dP_a)/(d theta)=12\ sec\ theta\ tan\ theta`

We are told

`(d theta)/(dt)=0.050`

So

`(dP_a)/(dt)=(dP_a)/(d theta)(d theta)/(dt)`

`=(12\ sec\ theta\ tan\ theta)(0.050)`

`=0.6\ sec\ theta\ tan\ theta`

When θ = 40° , this expression is equal to: 0.657 W/min.

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