Answer
$ \approx -0.60$
Work Step by Step
Write the chain rule.
$\dfrac{dP}{dt}=\dfrac{\partial P}{\partial L}\dfrac{dL}{ dt}+\dfrac{\partial P}{\partial k}\dfrac{dK}{dt}$
This implies that $\dfrac{dP}{dt}=(-1.911) \times k^{0.35} \times L^{-0.35}+0.25725 \times L^{0.65} \times K^{-0.65}$
This gives: $\dfrac{dP}{dt}=-1.203233025+0.607401286$
$\dfrac{dP}{dt} \approx -0.595831738$
Thus, we have $\dfrac{dP}{dt} \approx -0.60$
