Let $f$ be a smooth function, $f\colon\mathbb{R}^2\to \mathbb{R}$.
What is $\left[\frac{\partial f}{\partial x},\frac{\partial f}{\partial y}\right]$ ?
I want to say it's $0$ since $\frac{\partial f^2}{\partial x\partial y}=\frac{\partial f^2}{\partial y\partial x}$ but I am unsure about why for the two functions : $\frac{\partial f}{\partial x}$ ,$\frac{\partial f}{\partial y}$ the composition is the same...
Can someone please help with this ? [I didn't know what tag to give this post, hope it's ok]