I have the following differential:
$df = \lim \limits_{h \to 0} f[g(w+h)] - f[g(w)]$
after staring at this equation for about 40 minutes I have had the flash of insight that this could be$\frac{\partial f}{\partial g} \frac{\partial g}{\partial w}$, but I have no clue why. it just feels like for a small enough $h$, somehow multiplication would magically work like function composition. am I completely wrong?