Is it true that
$\frac{\partial}{\partial y} ( [\frac{\partial}{\partial x} F(x,y)]|_{x=0}) = [\frac{\partial}{\partial y} ( \frac{\partial}{\partial x} F(x,y))]|_{x=0} $
?
Seems easy but I can't affirm whether it is true or not.
Is it true that
$\frac{\partial}{\partial y} ( [\frac{\partial}{\partial x} F(x,y)]|_{x=0}) = [\frac{\partial}{\partial y} ( \frac{\partial}{\partial x} F(x,y))]|_{x=0} $
?
Seems easy but I can't affirm whether it is true or not.
It is. When differentiating with respect to $y$, we hold $x$ constant anyway. So we could first set $x=\text{constant}$ and then set the constant to zero, or just set $x$ to zero at once.