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! $$\frac{d}{dx} f(x) \neq f(x) \frac{d}{dx}.$$