What does the (∂X) symbol means in Matrix Cookbook?

Question

Check page 8 and equation 34 of Matrix Cookbook.

In this simple case we take the derivative of a matrix that is multiplied by a constant and we have: $\partial (aX) = a*(\partial X)$

Probably missing something crucial because I would expect ∂aX/∂X = a

So what does (∂X) represents exactly?

Answer 1

The notation:$$\partial (aX) = a*(\partial X)$$ is referred to ''differentials'' and means exactly that: $$ \frac{\partial (aX)}{\partial X} = a $$