We have the derivative operator which is defined as:
$$D^{\alpha}f(x) : = \frac{\partial^{|\alpha|}f(x_1,\ldots, x_n)}{\partial^{\alpha_1}x_1\ldots \partial^{\alpha_n}x_n}$$
where $|\alpha | = \alpha_1 + \ldots + \alpha_n $.
Now, how does the chain rule for $F\circ u$ look like?, i.e we have:
$$D^{\alpha}(F \circ u)(x_1,\ldots , x_n)$$