Let $f:\mathbb{R}^2\to\mathbb{R}$ be a smooth function (i.e. have derivatives of all orders).
Is the relation $$\frac{\partial}{\partial x}\frac{\partial}{\partial y}f = \frac{\partial}{\partial y}\frac{\partial}{\partial x}f$$ true?
I studied calculus a while ago and I don't remember if this is true, can someonem confirm ?