Question

Just a fun notation quirk to consider.
Is \(f'(g(x))\) equal to: \[
\frac{d}{dg}f(g(x))
\quad\text{or}\quad
\frac{d}{dx} f(x)\Bigg|^{x=g(x)}
\]

Answer 1

The trick is not to think too hard about it.

Answer 2

Interesting, I'm surprised I've never seen this before haha. It's beautiful.