Given the following differential operator, i am asked to rewrite it in polar coordinates
$\frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + 2\frac{\partial^2 f}{\partial x\partial y}$
I know how to get $\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}$ with respect to r and $\theta$ , but i have no ideea how to get $\frac{\partial^2 f}{\partial x^2}, \frac{\partial^2 f}{\partial y^2} and \frac{\partial^2 f}{\partial x\partial y}$ .