Surely the derivative is just ? Which is negative for , hence decreasing? Unless I'm misreading the question as I've no clue how logs appeared...
But your derivative is also always negative; either way it's decreasing.
Your sequence is obtained by sampling this function is decreasing because its derivative is negative. Because the function is decreasing the sequence obtained by sampling it at is also decreasing.
(you cannot differentiate a sequence because the index is a discrete variable and you need a continuous variable to differentiate)
RonL