how do you read partial derivative notation, from left to right or from right to left?

Question

how do you read partial derivatives? I have seen people reading from left to right, and have seen people reading from right to left.for example what does this equation mean $\frac{\partial f}{\partial x \partial y}$:

1)at first you differentiate with respect to x and then y, or

2)at first you differentiate with respect to y and then with respect to x?

earlier I knew the first one, now I have read the authors used 2).

Answer 1

The standard notation is the $2)$: $$ \frac{\partial^2 f}{\partial x \partial y} := \frac{\partial}{\partial x} \left(\frac{\partial f}{\partial y}\right) $$

EDIT

Other notations:

• $f_{yx}=\frac{\partial^2 f}{\partial x \partial y}$
• $\partial_x \partial_y f=\frac{\partial^2 f}{\partial x \partial y} $