求z=f(x+ay)+g(x-ay)二阶导数

Question

如题所述

Answer 1

Z = f(x+ay) + g(x-ay) u = x+ay v = x-ay Z = f(u) + g(v)
∂Z/∂x = (∂f/∂u)(∂u/∂x) + (∂g/∂v)(∂v/∂x) = ∂f/∂u + ∂g/∂v (1)
∂²Z/∂x² = ∂²f/∂u² + ∂²g/∂v² (2)
∂Z/∂y = (∂f/∂u)(∂u/∂y) + (∂g/∂v)(∂v/∂y) = a ∂f/∂u - a∂g/∂v (3)
∂²Z/∂y² = a²∂²f/∂u² + a²∂²g/∂v² (4)
∂Z²/∂x∂y = a∂²f/∂u² -a ∂²g/∂v² (5)本回答被网友采纳