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this post was submitted on 06 Jun 2025
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You cannot differentiate a sum when the variable being differentiated is used to define the number of terms in the sum — unless you rewrite the sum as a closed-form, continuous expression. Even in Sigma notation as you used.
The act of summing “x terms” as you expressed in your sum is not itself a differentiable process.
Once you turn it into a continuous function (in this case x^2), then you can differentiate it.
The Leibnitz rule doesn’t do anything here because you still have an unextractable “x” that’s defining your summation.
That makes sense, thanks. I knew someone would know better than me how to interpret that.