i have the following problem.
Consider $f(\frac{|x|^2}{2})$ a radial function on $\mathbb{R}^2$ where $f:\mathbb{R}_+\to\mathbb{R}$. Then my book says that $$\Delta f-\langle x,\nabla f\rangle$$ is basically the same as $2xf''(x)+(1-2x)f'(x)$
Can someone elaborate on that or give me an example for $f$ to understand this?