Ex 93

In the project on page 344 we expressed the power needed by a bird during its flapping mode as
\[P(v, x, m) = Av^3 + \frac{B(mg/x)^2}{v}\]
where \(A\) and \(B\) are constants, \(v\) is the velocity, \(m\) is the mass, 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.