if i am not wrong, there is only one problem - sum to x (x times)
when we write it in a bit more concise but equivalent notation - d/dx sum_1^x x it basically becomes x^2 again. It is kinda a a=a proof, so not very interesting but that is the only problem. since sum is happening a variable number of times, we can not really let it loose.
in a more reasonable wording - what the image showed was interchanging differentiation and sum (like instead of doing sum after diff, instead of before), and such operations are allowed, but if the sum and diff are independent (not based on same variables).
this interchange works if you used some other variable which is independent of x
if i am not wrong, there is only one problem - sum to x (x times)
when we write it in a bit more concise but equivalent notation - d/dx sum_1^x x it basically becomes x^2 again. It is kinda a a=a proof, so not very interesting but that is the only problem. since sum is happening a variable number of times, we can not really let it loose.
in a more reasonable wording - what the image showed was interchanging differentiation and sum (like instead of doing sum after diff, instead of before), and such operations are allowed, but if the sum and diff are independent (not based on same variables).
this interchange works if you used some other variable which is independent of x