I found a question:
Suppose that $z= e^{x+y}$. Show that the result of differentiation $z$, $m$ times with respect to $x$ and $n$ times with respect to $y$ is
$$\frac{\partial^{m+n}z}{\partial x^m\,\partial y^n} = e^{x+y}$$
When I think about it, it is right because any differentiation either with respect to $x$ or $y$ is still $e^{x+y}$, and through the chain rule of $x+y$ , it will always become 1. So, it will be $e^{x+y}$ times Q $1$’s every time you differentiate it $Q$ times. Now, how does one show it is correct.