Detection of elementary functions

In order to learn several types of derivatives, in particular the derivative of the composition of two different functions we need to understand what a composition of functions is.

Let $f(x)=\sin 2x$

In this case the function is a composition of two functions:$$f(x)=\sin x \\ h(x)=2x$$

The composition is: $f(x)=g(h(x))$

It is read: $f(x)$ is equal to $g$ of $h(x)$

Let $f(x)=(\sin 3x)^2$

In this case $f(x)$ is a composition of three functions:$g(x)=x^2$, $h(x)=\sin x$, $t(x)=3x$

That is: $$h(t(x))=\sin 3x \\ f(x)=g(h(t(x)))=(\sin 3x)^2$$

Let $f(x)=\cos x^3$

Can you already identify two elementary functions that compose $f(x)$? $$f(x)= \cos x \\ h(x)=x^3$$