Question

求大神帮忙解答

Answer 1

设u=3x+2y
v=xsiny
则z=f(u,v)
令∂z/∂u=f1，∂z/∂v=f2
∂z/∂x=∂z/∂u * ∂u/∂x + ∂z/∂v * ∂v/∂x=3f1+siny f2
∂z/∂y=∂z/∂u * ∂u/∂y + ∂z/∂v * ∂v/∂y=2f1+xcosy f2
令∂f1/∂u=f11，∂f1/∂v=f12，∂f2/∂u=f21，∂f2/∂v=f22
∂²z/∂x∂y=3(∂f1/∂u * ∂u/∂y +∂f1/∂v * ∂v/∂y)+siny(∂f2/∂u * ∂u/∂y +∂f2/∂v * ∂v/∂y)
=3(2f11 + xcosy f12) + siny(2f21 + xcosy f22)