Derivatives in higher order, very confused!!

O

OrangeOne

New member
Joined
Sep 8, 2010
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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!
 
OrangeOne said:
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 <<< satisfy what? You do not have an equation or condition to satisfy.




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!
Click to expand...
 
OrangeOne said:
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

Now find u*f[sub:3cd6ofvr]u[/sub:3cd6ofvr] and v*f[sub:3cd6ofvr]v[/sub:3cd6ofvr] and do the grunt work (algebra)

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.

Are you asking us to do the grunt work (algebra) - or have you done those and not showing those to us?

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!
Click to expand...
 
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