d(x^2)/dx = 2x;
now we also know that
x^2 = x*x = (x+x+x+x+x+x+x+-----------)x times;
thus y differentiating both the side
d(x^2)/dx = (1+1+1+1+1+1+1+----------)x times;
2x = x;
2 = 1
:(
what the hell is this
think about it
think about it
I will be happy if you prove it wrong because i dont want my studied mathematics to be a waste
reply it i will post my comments at last its an easy answer
ReplyDeleteadding x number of times is also a function of x and needs to be differentiated separately.
ReplyDeletesee
ReplyDeletey=x;
on diffrentiating we get 1;
n here no probs in its domain
while if it iz written as
y=1+1+1......X times
on diff. we get zero....
because the second function has integral
domain,,,
and iz non diffrentaiable,,,,
hence da ans to above ques qz wel,,
i liked the response for this question
ReplyDeletebut sorry friends for my replies we have to wait at least a week as i want more people to try on this
I would also request vaarij to post his views as i want every body to know about everybody's view
dont just solve it verbally use the facilities of web 2.0 :) ;)
Both Anshul and Pankaj are right
ReplyDeletebut clearing the anshul's oint actually addng any thing x times is also a function whose differentiation is not zero adding n times (where n is a contant is also a function) with zero differentiation
interpretation 2
Pankaj is also right because adding anuthing x times is only valid for intergers and not the real nos
so the doimain is discrete and therefore not differentiable
interpretation 3
one of my friends again argued that instead of x times we can also right (x+x+x+x+x+....)[x] times + x*{x}
where [] greatest integer function
{} fractional part
and according to him this covers the whole domain
so my friend lets start differentiating it
(1+1+1+1+1.....)[x] times + 1*{x}+x*d({x})/dx
= [x] + {x} + x = x+x = 2x = lhs
d({x}/dx is diffrentiable at non integer domain which is continuous between 2 integers
so thus if we take {x} into account we will get answer for real nos.
The graph will be posted in the next post