The Del Operator

If we look at del, we notice it's made up of operators and vectors.

But what's an operator? The differential operator \( \frac{d}{dx} \) acting on a function \( f(x) \) determines the derivative of \( f(x) \) w.r.t. \( x \). $$ \frac{d}{dx} f(x) \rightarrow \frac{d f(x)}{dx} $$ Operators are non commutative which means order matters! $$ \frac{d}{dx} f(x) \neq f(x) \frac{d}{dx}. $$