Quote by I like Serena
As MathematicalPhysicist already said, the first mistake is when you moved d/dn to the other side of the summation symbol.
This is not allowed, because the summation is dependent on n.

Thanks. I forgot about that.
Quote by I like Serena
You made another mistake when you differentiated the expression dependent on t with respect to n.
Since the expression is not dependent on n, the result is zero.

Oops.
Quote by I like Serena
How did you get WolframAlpha to say that?
I do not get that.

I think I know what happened. It must have again considered d as constant rather than an infinitesimal.There seems to be a simpler solution using the second fundamental theorem of calculus and that would yield
[tex]\frac{1}{\mbox{ln}(n)}[/tex]
which is the answer given by you.