I am given variance $\sigma_x$ and function $y=f(x)$
According to my book, the following equation gives the new variance of $y=f(x)$. But I'm not sure what this notation means, as in what this combination of $\partial$'s and $d$'s represents.
$$\Large{\sigma_y^2=\frac{\partial df^2}{\partial x} \sigma_x^2}$$
I understand that $\frac{\partial g}{\partial u}$ is the partial derivative of $g$ w.r.t $u$, but what does it mean when $g = df^2$ ?