Product of the cosine function and the cosine of sine function and the cosine of sine of sine function and the cosine of sine of sine of sine function

The product of the cosine function and the cosine of sine function and the cosine of sine of sine function and the cosine of sine of sine of sine function is the product of four functions: the cosine function, the cosine of sine function, the cosine of sine of sine function, and the cosine of sine of sine of sine function.

This function is also the derivative of the sine of sine of sine of sine function.

Notation
It is notated as $$x \mapsto \cos \left( x \right) \cos \left( \sin \left( x \right) \right) \cos \left( \sin \left( \sin \left( x \right) \right) \right) \cos \left( \sin \left( \sin \left( \sin \left( x \right) \right) \right) \right)$$