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

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).

The standard notation is the $$2)$$: $$\frac{\partial^2 f}{\partial x \partial y} := \frac{\partial}{\partial x} \left(\frac{\partial f}{\partial y}\right)$$
• $$f_{yx}=\frac{\partial^2 f}{\partial x \partial y}$$
• $$\partial_x \partial_y f=\frac{\partial^2 f}{\partial x \partial y}$$
• And $\frac{\partial}{\partial x}(\frac{\partial f}{\partial y})=f_{yx}$, right?
• @bof Yes: $$f_{yx}= (f_y)_x=\frac{\partial}{\partial x} f_y =\frac{\partial}{\partial x} \frac{\partial f}{\partial y} = \frac{\partial^2 f}{\partial xy}$$ Jun 13, 2020 at 11:06