## Standard Error

Calculate the value of f and its standard error $s_{\bar{f}}$ assuming the standard error of x and y, $s_{\bar{x}}$ and $s_{\bar{y}}$ are independent and random and from the given values and standard errors for x and y.

1. $f=x^2$ for $x=25\pm1$

So using the formula we have for it, I get ${s_{\bar{f}}}^2={(\frac{\delta f}{\delta x})}^2 s_{\bar{x}}=(2x)^2 s_{\bar{x}}=50s_{\bar{x}}$

First, is that correct thus far?
Second, what is $s_{\bar{x}}$? Is it just the 1 from the $\pm 1$ in the uncertainty of f?