Given $u=\sin 3x \cos 4y$
Step 1:
$\large\frac{\partial u}{\partial y}$$=-4 \sin 3x \sin 4y$
$\large\frac{\partial^2 u}{\partial x \partial y}$$=-12 \cos 3x \sin 4 y$
Step 2:
$\large\frac{\partial u}{\partial x}$$=3 \cos 3x \cos 4y$
$\large\frac{\partial^2 u}{\partial y \partial x}$$=-12 \cos 3x \sin 4 y$
Step 3:
$\large\frac{\partial^2 u}{\partial x \partial y}=\frac{\partial^2 u}{\partial y \partial x}$