Originally Posted by **Glavien** If I want to calculate the uncertainty in X given that X = 2/(A*B)^2, how would I do it? I know the uncertainties in A and B and want to find out the uncertainty in X. Thanks! |

Let $\displaystyle u = AB$,

$\displaystyle \frac{\delta u}{u} = \left[\left(\frac{\delta A}{A}\right)^2 + \left(\frac{\delta B}{B}\right)^2\right]^{1/2}$

Let $\displaystyle X = \frac{2}{u^2} = 2u^{-2}$,

$\displaystyle \frac{\delta X}{X} = -2 \frac{\delta u}{u} = -2 \left[\left(\frac{\delta A}{A}\right)^2 + \left(\frac{\delta B}{B}\right)^2\right]^{1/2}$

Therefore,

$\displaystyle \delta X = -2X \left[\left(\frac{\delta A}{A}\right)^2 + \left(\frac{\delta B}{B}\right)^2\right]^{1/2}$