Question

If z=f(x,y) where x=u^2-v^2 and y=2uv then prove that ​

Answer 1

Answer:

If z=f(x,y) where x=u^2-v^2 and y=2uv then prove that

Answer 2

Answer:

4u²+4v²

Step-by-step explanation:

Given, x=u²+v² and y=2uv

We know, Jacobian of x,y w.r.t u and v is :∂(x,y)/ ∂(u,v)

which we get as  $\left[\begin{array}{ccc}2u&-2v&\\2v&2u&\\\end{array}\right]$=4u²+4v²