folks.
I have been trying to figure out how to take a derivative of a function of vector norm with respect to vector.
Basically, I know the following basic derivatives.
$\frac{\partial}{\partial \bf r} \lvert\lvert \bf r \rvert\rvert = \frac{\bf r}{\lvert\lvert \bf r \rvert\rvert}\\$
$\frac{\partial}{\partial \bf r} \frac{\bf r}{\lvert\lvert \bf r \rvert\rvert} = \frac{\bf I}{\lvert\lvert \bf r \rvert\rvert} - \frac{\bf r \otimes \bf r}{\lvert\lvert \bf r \rvert\rvert ^3}$
Starting from those, I want to know how to differentiate the following function with respect to vector,
$\frac{\partial}{\partial \bf r} \frac{1}{\lvert\lvert f(\bf r) \rvert\rvert} = \frac{\partial}{\partial \bf r} \frac{1}{\lvert\lvert \bf r \times (\bf r \times \bf r' ) \rvert\rvert} = ?$
Thank you and it would be also appreciated if you can share the materials or text book that I can use to study advanced vector or tensor calculus?
Thank you.