Tensor Derivatives, General Relativity

[Reedeegi]

Homework Statement

Given U^$$\alpha$$ = (1+t², t², t√2, 0), calculate
$\partial_{\beta}D^{\alpha}$

Homework Equations

$\partial_{\beta}D^{\alpha}$ = $$\frac{\partial D^{\alpha}}{\partial x^{\beta}}$$

The Attempt at a Solution

I don't really know where to start, the indices drive me insane. All I need is the method, not the answer.

 

[tiny-tim]

Given U^$$\alpha$$ = (1+t², t², t√2, 0), calculate
$\partial_{\beta}D^{\alpha}$

Hi Reedeegi!

(have a a curly d: ∂ and an alpha: α and a beta: β )

I assume you mean that at the point (t,x,y,z), the vector U is (1+t², t², t√2, 0) …

then for example ∂_tU^y = ∂U^y/∂t = ∂(t√2)/∂t = √2 …