Chapter 14.3, Problem 89E

In the project following Section 4.7 we expressed the power needed by a bird during its flapping mode as

$P(v,x,m)=A{v}^3+\frac{B{(mg/x)}^2}{v}$

where $A$ and $B$ are constants specific to a species of bird, $v$ is the velocity of the bird, $m$ is the mass of the bird, and $x$ is the fraction of the flying time spent in flapping mode. Calculate $\partial P/\partial v,\partial P/\partial x$ , and $\partial P/\partial m$ and interpret them.