we all know d/dx ( x ) = 1
d/dx(x^2) = 2x
and so on..
what if i write like this
x= 1 + 1 + 1+ 1............x times
and x^2 = x +x +x +x ............x times

now when we differentiate both, we come to a different ans..so where are we going wrong ?

Question

we all know d/dx ( x ) = 1
d/dx(x^2) = 2x
and so on..
what if i write like this 
x= 1 + 1 + 1+ 1............x times
and x^2 = x +x +x +x ............x times

now when we differentiate both, we come to a different ans..so where are we going wrong ?

anonymous · Answer

x^2 = x +x +x +x ............x times  is for integers only

anonymous · Answer

true!!
 yet again..

anonymous · Answer

this is a series. The differentiation for them is only working the way you expect if the series is uniformly convergent, which is not the case in any of two examples you put

anonymous · Answer

@Aryang