# Covariance between x and f(x)?

1. May 7, 2012

### hb1547

1. The problem statement, all variables and given/known data
As part of an assignment, I have to determine propagated error of some function:
$f(x,t)$
I did it first with x & t being completely uncorrelated, but now I'm given x as a function of t, $x(t)$, and have to do the same.

2. Relevant equations
I know the linear approximation for finding the uncertainty $\sigma_f$, all I need is the covariance term.
The equation x(t) itself is simply $x(t) = a \sqrt{t}$, where a is just a constant.

3. The attempt at a solution
I seem to be having a hell of a time Googling to find a way to calculate the covariance between t and x(t).

Last edited: May 7, 2012
2. May 8, 2012

### I like Serena

Hi hb1547!

I do not believe you need the covariance.
Let's define g(t)=f(x(t),t).
Then the uncertainty in g(t) is g'(t)σt.

Do you know how to calculate g'(t)?
It consists of a couple of partial derivatives and the chain rule...