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 $$f(x)$$? $$$f(x)= \cos x \\ h(x)=x^3$$$