After literally hours of "no, and what and how", I need help with the following task:
f(u,v)= g(x(u,v),y(u,v))
x(u,v)= u^2- v^2
y(u,v)= 2uv
Expressing f'u and f'v as partial derivatives of g I get:
f'u= (dg/dx)*(dx/du) + (dg/dy)*(dy/du)
f'v= (dg/dx)*(dx/dv) + (dg/dy)*(dy/dv)
Now I'm supposed to find all functions f that satisfy u*f'u - v*f'v= 0
The hardest part (which confuse me the most because there are so many steps involving the chain rule is the following): Express f''uu+ f''vv through partial derivatives of g. Simplify as much as possible.
Please help me with either of the tasks, I need this by monday and I'm so confused and tired of staring at this task!
f(u,v)= g(x(u,v),y(u,v))
x(u,v)= u^2- v^2
y(u,v)= 2uv
Expressing f'u and f'v as partial derivatives of g I get:
f'u= (dg/dx)*(dx/du) + (dg/dy)*(dy/du)
f'v= (dg/dx)*(dx/dv) + (dg/dy)*(dy/dv)
Now I'm supposed to find all functions f that satisfy u*f'u - v*f'v= 0
The hardest part (which confuse me the most because there are so many steps involving the chain rule is the following): Express f''uu+ f''vv through partial derivatives of g. Simplify as much as possible.
Please help me with either of the tasks, I need this by monday and I'm so confused and tired of staring at this task!