I feel stupid for having to ask this, but does anybody have any idea how to handle
$$\frac{d}{x}\sum\_{n=k}^{g(x)}f(n,x)?$$
Example:
$$\frac{d}{dx}\sum\_{n=6}^{i^2+2i} \frac{1}{\ln{(i^2)}-\ln{\ln n}}.$$
If we were able to separate the summand into two functions, one with only $i$ as a variable, and one with only $n$ as a variable, this would be super simple. But it is not always the case. Any ideas?



Derivative of Sum over Variable of derivative
This reminds me uncomfortably about a remark that Terry Tao made in [this answer](https://mathoverflow.net/questions/40082/why-do-we-teach-calculus-students-the-derivative-as-a-limit/44572#44572) about the importance of teaching the derivative as a limit: at least one person tried to prove Fermat's Last Theorem by differentiating with respect to the exponent. It does not make sense.


The reason why it does not: the derivative is something that is properly defined for **real** (or complex) variables. If you're variable is an integer, derivatives will not make sense.


There may objects that are analogous to the derivative in some ways, but you cannot carelessly apply derivative rules.


