Final answer:
The derivative of the function f(x) = ln(sin(8)) is zero since sin(8) is a constant and the natural logarithm of a constant is also a constant.
Step-by-step explanation:
The student has asked to find the derivative of the function f(x) = ln(sin(8)). To find the derivative of this function, we must first recognize that the derivative of a constant is zero. Since sin(8) is a constant because 8 is a constant value and not a variable, and the natural logarithm of a constant is also a constant, the derivative of the function is simply zero.
The derivative of the function f(x) = ln(sin(8)) is zero since sin(8) is a constant and the natural logarithm of a constant is also a constant.
This conclusion uses properties of logarithms and differentiation rules, as the natural logarithm and the exponential function are inverse functions, each nullifying the effects of the other as part of their fundamental relationship.