Writing "$\nabla f$" or "$\operatorname{grad} f$" When hand-writing the gradient of $f$ as "$\nabla f$" or "grad $f$", is it necessary to indicate that it is a vector using the usual vector markings (cap, arrow, wavy line, etc.)?

It should be considered obligatory to write, for example  $\vec{a}$ or $\mathbf{a}$, when you're writing in a context in which vectors and vector-valued functions are generally written that way.  But that is not always done.  The style should be consistent throughout the document.
However, notice that the $f$ in $\nabla f$ is scalar-valued.  The expression $\nabla f$ is vector-valued, and that is indicated by the meanings of the symbols.
