x+x+..+x(xtimes)=x^2 ..differentiating both side.. 1+1+..+1(x times)=2x...x=2x...1=2... whats wrong?

Answer 1

you can differentiate only continuous functions...here left side(x+x+x+...) is not continuous hence non differentiable..

Answer 2

Yes, something is hiding in the +..+ that didn't get differentiated. That is the +..+ is really a variable of some sort which is not clearly specified. It is not just a fixed number of x's, it is a variable number of x's. It would be exactly (x-3) x's. This is just a long hand way of writing (x-3)x = g(x). So g'(x) = 2x^2-3!

Note that if you write x+x+x+x+x+x+x+x+x+x+x+x+x(13 times) it is just 13x and the derivatives are 1+1+1+1+1+1+1+1+1+1+1+1+1 = 13 and 13x'=13

Answer 3

the problem is that you are taking a derivative with respect to x,
so the left hand side depends on x in two ways,
in each summand (of course) but also in the number of times you are adding,
and therefore you need to differentiate both....

Answer 4

The above identity is only true if x is a positive integer. It make no sense to differentiate a function defined over the positive integers only.

Answer 5

The problem is that "(x times)" is not a differentiable function.

If you knew how many x's you were adding on the left, then that number is a constant, and you can do exactly what you're proposing. But in this case, you don't, so you can't. Sorry. :)

Answer 6

Here x is variable where (xtimes) is a number which is not variable

Answer 7

Function is discontinueous

Answer 8

Lhs is not a continuous function.Differentiating this has no meaning and it is not valid and hence the discrepancy.

Answer 9

you can draw a tangent line to y=x^2
But you can not draw a tangent line to a line.

Answer 10

no one nos