Two Forms of the Chain Rule
The chain rule is one of the most powerful tools for computing derivatives.
There are two forms of it:
 If $f$ and $g$ differentiable functions, then
$$ \Big(f\big(g(x)\big)\Big)' = f'\big(g(x)\big) \cdot g'(x).$$

If $y=f(u)$ and $u=g(x)$, then $$\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}.$$

The two versions mean the exact same thing, but sometimes it's easier
to think in terms of one or the other. The first version is best for
computing derivatives of expressions like $(5+3x)^5$ of
$\ln(3+\cos(x))$. The second version is best for understanding related
rates or logarithmic derivatives.
We will first develop Version 1, and then discuss how to convert to Version 2.
