Chapter 14.3, Problem 93E

In the project on page 344 we expressed the power needed by 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 ∂P/∂v, ∂P/∂x, and ∂P/∂m and interpret them.