Question

Hi guys, what do you think about this problem
if differentiate \(\huge \rm (x^2)'=2x\)
if i think of \(\huge \rm x^2\) as \(\huge \rm x.x=(x+x+x+x............x)\) and then I differentiate it \(\large \rm (x+x+x+....+x)'=1+1+1+.....+1=x\)
what is the problem here?

Answer 1

it is legit that differentiating the sum is the sum of derivative! so where is the issue

Answer 2

@ganeshie8

Answer 3

wow its really something wrong :P

Answer 4

Have you ever thought about it? it is interesting thing

Answer 5

i thought about it :O
i said something wrong xD

Answer 6

oh! so what did you think was wrong here?

Answer 7

:P lol it a bit complex how things get to this
but it must be something not really that big is the issue here

Answer 8

derivative function as you have applied, is defined for a real and complex functions only!

Answer 9

it is true x.x=x+x+x+...+x
x times

Answer 10

according to our arithmetic laws

Answer 11

ok , X is variable
how u can be sure it applies the sum of x times ?
it might be some negative number
so let x=-3
x^2=-3*-3
can u express this in sum xD
u have to take |x| lol sort of creepy

Answer 12

whereas, in your second line, you treat the function y=x*x as a integer function

Answer 13

this is also real @Michele_Laino so that's not the issue
x^2=x.x not problem about that

Answer 14

this is one of the classic fake proofs for proving 1=2

Answer 15

yeah , nice proof though

Answer 16

No x variable can be written as x^2 can be written as x.x
or any other form no problem as far as i know

Answer 17

ok write this in arithmetic way
(1/2)^2

Answer 18

@ganeshie8, my prof give us this! he said it is not the type of proving 1=2

Answer 19

1/2.1/2? the same as 1/4

Answer 20

If x^2 is a real function, for example, you can not write x*x=x+x+...x,
because x is a real number, and the set of real number is not numerable.

Answer 21

ok now lets this of the differential definition hmm

Answer 22

the prof said it is about how we differentiated the x+x+x+...+x

Answer 23

can you please come and help me on a problem

Answer 24

y=(x^2)
dy/dx=2x

x.x=x+x+x+x...+x ( x times )
think of it like
(gf)' xD

Answer 25

So the LHS is 2x but the right hand side is what?

Answer 26

yeah that will work, then use the product rule

Answer 27

@xapproachesinfinity If x^2 is a real function, for example, you can not write x*x=x+x+...x,
because x is a real number, and the set of real numbers is not numerable

Answer 28

@Michele_Laino I said there is no problem whatsoever about how we know a function
this is a differentiation problem

Answer 29

so the LHD is good! no problem about it
the right hand side causes the problem lol
something is wrong we we differentiate that sum

Answer 30

see this
http://math.stackexchange.com/questions/1096/where-is-the-flaw-in-this-argument-of-a-proof-that-1-2-derivative-of-repeated

Answer 31

Oh great! I guess i kind of see the flaw of this problem