FYI the natural log is written as ln(x) - that's a lower case L.
Looking at the domain of the original equation it would appear that no values satisfy the equation since the argument must be positive.
The range of sin(x) is . We can immediately discard the negative values (and 0) of sin(x) to satisfy the inner bracket. For then and as mentioned above the argument of a log must be positive so all values of x lie outside the domain of y.
It would then follow that if the original function cannot be satisfied then there must be no derivative
Hope this makes sense and for what it's worth I get the same value for the derivative as you: