The derivative of #y=ln(2)# is #0#.

Remember that one of the properties of derivatives is that the derivative of a constant is always #0#. If you view the derivative as the slope of a line at any given point, then a function that consists of only a constant would be a horizontal line with no change in slope. That is why the derivative of any constant is #0#, meaning no changes anywhere.

If the natural log function, #ln#, only has a constant inside its parenthesis, then it is itself only a constant number. #ln(2)# is an actual number, with a value of around #0.6931472#. Because of that quality of logarithms, we know that #ln(c)# (with #c# being any constant located in it's domain) will always have a derivative of #0#.