
Standard Error
Calculate the value of f and its standard error $\displaystyle s_{\bar{f}}$ assuming the standard error of x and y, $\displaystyle s_{\bar{x}}$ and $\displaystyle s_{\bar{y}}$ are independent and random and from the given values and standard errors for x and y.
1. $\displaystyle f=x^2$ for $\displaystyle x=25\pm1$
So using the formula we have for it, I get $\displaystyle {s_{\bar{f}}}^2={(\frac{\delta f}{\delta x})}^2 s_{\bar{x}}=(2x)^2 s_{\bar{x}}=50s_{\bar{x}}$
First, is that correct thus far?
Second, what is $\displaystyle s_{\bar{x}}$? Is it just the 1 from the $\displaystyle \pm 1$ in the uncertainty of f?