Am I correct in writing the chain rule for univariate functions this way?

Question

I was just making some notes on an online course for myself, and (trying to remember my university calculus), wrote down the chain rule this way:

$$ \frac {\textrm{d}}{\textrm{d}x}f(g(x)) = \frac {\textrm{d}f(g(x))}{\textrm{d}(g(x))} \cdot \frac {\textrm{d}g(x)}{\textrm{d}x} $$

Am I correct or is there something wrong with this expression?

Answer 1

A symbolic expression is to be suggestive and mnemonic; of importance is what defines the symbolic expression. If you know what you are doing and are consistent in your notation, then there is nothing wrong with it.

I would suggest writing $(f\circ g)' = (f' \circ g)\cdot g'$ or $D(f\circ g) = (Df \circ g)\cdot Dg$ instead; this is more useful when it comes to maps $\mathbb{R}^{n} \to \mathbb{R}^{m}$.