# Is the Leibniz's notation wrong in the Hessian video?

Week 3
Lesson 2: Newton’s Method
Video: The Hessian

At round time 3:53 the Leibniz’s notation for partial derivatives is shown. The second partial derivative w.r.t x and y the notation should be other way around.

fxy(x, y) fyx(x,y)
In Leibniz’s notation looks wrong to me.
I also cross checked it here (the post would not let me paste the link):

google search: leibniz notation for 2nd partial derivative
scroll down to and click: 13.3 Partial Derivatives from Mathematics Libre Text
Scroll to section: Higher-Order Partial Derivatives
and the correct notation is shown?

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I think you are right, there must be a typo.
Rate of change of f'_x(x, y) w.r.t. y is the y-partial derivative of f'_x i.e.
\displaystyle \frac{\partial }{\partial y} \left( \frac{\partial f}{\partial x} \right) = \frac{\partial^2 f}{\partial y \partial x}
and vice versa.

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Yes, though these derivatives almost always give the same answer but they mean two different things !. Instructor should fix them.

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