Propagation of Error If I have a function $$f(x,y)=\sqrt{x^2+y^2}$$ with error in $x$ be $\Delta x$ and error in $y$ be $\Delta y$, then how do we calculate ${\Delta f}$?
I know if we have $$f(x)=x^n$$, then I at least that $\frac{\Delta f}{f}=|n|\frac{\Delta x}{x}$. I have no idea how to proceed. 

The error is typically approximated using the differential; i.e. the first-order term of the Taylor series:
$$ \Delta f \approx df(\Delta x, \Delta y) = \frac{\partial f}{\partial x} \Delta x + \frac{\partial f}{\partial y} \Delta y.$$
For your particular $f$ we have $\partial f / \partial x = x/f, \partial f / \partial y = y/f$.
