During my studies years ago I came over a formula that states something like if $x_i$ are independent normally distributed variables with variances $\sigma^2_i$ and $f(x_i)$ is differentiable (and probably otherwise "good" I don't remember), then the variance of $f$ would be something along the lines of $$\sum_i\left(\frac{\partial{f}}{\partial{x_i}}\right)^2\sigma^2_i$$
but I'm not sure neither about the powers not the multipliers , the only thing I remember that it involved partial derivatives.
Does anyone know the correct formula? Thank you in advance.