Help with contravarient vector transformation

[fys iks!]

Homework Statement

Let A = <2,1> be a vector with contravarient components at a point P with coordinants u1 = 1 , u2=1. Find the components a-1,a-2 (-1 and -2 are upstairs) of this vector with respect to the coordinates u-1 = sqrt((u1)^2 + (u2)^2) and u-2 = arctan(u2/u1).

Homework Equations

V^m(y) = (dy^m/dx^n) * V (x)^n

The Attempt at a Solution

I got the second component to be -1/2 which is correct but for the first component i keep getting 2/2^(1/2) but the answer is 3/2^(1/2).

The derivative of u-1 wrt u1 is:

1/2 [ (u1)^2 + (u2)^2) ]^(-1/2) * (2*u1)

then when i plug in u1=1 and u2 = 1 you get 1/(2^(1/2)). Then i multiply that by the a1 component 2 and this is how i got my answer.

Can anyone see where i went wrong?

 

[twofish-quant]

Remember that there is an implied summation over terms for u1 and u2 so that I think you are missing a term for u-1 with respect to u2.

 

[fys iks!]

If i sum over the terms then multiply by 2 i get 4/(2^(1/2)).

but i get the 3/2^(1/2) if i multiply the first term by the 2 then sum then second term.
but i don't know why you would do it this way since it breaks the order of operations.

also i didnt do a summation when i did the second component and i got the right answer.

I know that there should be a summation, but I am just not sure where/ when it should occurs

Thanks