Chapter 14.3, Problem 93E

In the project on page 271 we expressed the power needed by a bird during its flapping mode as

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

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.