Say I have a 2 dimensional cartesian laplace operator for a function
$\Delta f = \frac{\partial^2 f}{\partial X^2} + \frac{\partial^2 f}{\partial Y^2}$
Part of the exercise is to scale the coordinates with a constant ie $X = kx, Y = ky$
How do you pull out k from the laplace operator? My suggestion was:
$\Delta f = k(\frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2})$
However this was clearly wrong, and I have a hard time finding information on how this would work. Thankful for any explanation!
(this is to simplify the expression that the laplace operator is in, but it's unnecessary info for my question)