I have a function
$$ h(\phi)=g(\epsilon + f(1-\phi)). $$
Here, $\epsilon$ is a constant, and $g$ and $f$ (like $h$) are functions of a single variable. The variable here is $\phi$.
I'm being told that
$$ h'(\phi)=-g'(\epsilon+f(1-\phi))f'(1-\phi). $$
How does one arrive at this conclusion? The negative sign is what's confusing me.
If you think it'd be helpful, I'd be happy to share context and/or my work on this (i.e., what I think the derivative should be). Just ask.
In theory, though, there is enough information here to answer the question.