Given this non-linear first order differential equation:
$$y' + f(x)y + g(x)y^n = 0.$$
How do I rewrite this to a linear differential equation by using the following substitution:
$u = y^{1-n}$.
I know that it might be helpful to first express $u'$ in terms of $y$ and $y'$ but I'm not sure how to proceed.