The second one is equivalent to the original statement.
If and are constants, while you could technically use the product rule, I would simply use the rule:
where is an arbitrary constant.
You will get the same result using the product rule since the derivative of a constant is zero.
A trig. function of a constant is just a constant, so its derivative would be zero.
How deeply you must go is determined by how many "compositions" you have.
The two terms you began with have 3 compositions each. Let's look at the first term:
If we let:
then we may state:
The chain rule tells us then: