I am completely confused by a second order directional derivative in pola coordinate. I need to find below derivative:
$\partial_i \partial_j f(\rho) = ?$
$i$ and $j$ are component of polar coordinate (say $\rho$ and $\phi$).
I can find gradient of $f(\rho)$ which is a tensor as below:
$\nabla f(\rho) = \partial_{\rho} f(\rho) \hat{\rho}$
What is solution to the second order partial derivative? I know that it is a tensor but I don't know how to calculate it. Any answer is highly appreciated.(Also introducing a reference for thing like laplacian of a second rank tensor is really appreciated)