Chapter 14 - Partial Derivatives - 14.5 The Chain Rule - 14.5 Exercises - Page 985: 42

$$\approx -0.60$$

We need to use the chain rule as follows: $$\dfrac{dP}{dt}=(\dfrac{\partial P}{\partial L})(\dfrac{dL}{ dt})+(\dfrac{\partial P}{\partial k})(\dfrac{dK}{dt}) \\=(-1.911)k^{0.35}L^{-0.35}+0.25725 L^{0.65}K^{-0.65} \\=-1.203233025+0.607401286 \\ \approx -0.595831738 \\ \approx -0.60$$