notation for partial derivatives (comma)

Question

Can anyone help me understanding the following notation of derivatives in detail?

For $f: \mathbb{R}_+$x$\mathbb{R} \rightarrow\mathbb{R}$:

$f_{,2}(t,x)$ or $f_{,22}(t,x)$

Thank you!

Answer 1

It is $$f_{,2}(t,x)=\dfrac{\partial f}{\partial x}$$ and

$$f_{,22}(t,x)=\dfrac{\partial^2 f}{\partial^2 x}.$$

Another cases:

$$f_{,1}(t,x)=\dfrac{\partial f}{\partial t}$$ and

$$f_{,12}(t,x)=\dfrac{\partial^2 f}{\partial t\partial x}.$$

That is, $$,_i=\dfrac{\partial}{\partial x_i}$$ and

$$,_{ij}=\dfrac{\partial^2}{\partial x_i\partial x_j}.$$