i think ur logic is flawed

  mana question??

why not like this??

2 * 2 = 2+2;
2 * 3 = 2+2+2;
2 * 4 = 2+2+2+2;
...
x * y = x+x+x+....+x+x (y number of times)
 

d/dx(x^2)=2x
d/dx(x+x+x+...+x+x)=1+1+1+1+...+1+1+1 (2x number of times)
which equals to 2x

therefore,
2x=2x,
2=2

d/dx(x^2)=2x
d/dx(x+x+x+...+x+x)=1+1+1+1+...+1+1+1 (2x number of times)

2x because of d/dx(x^2)=2x

d/dx(x^2) = d/dx(x+x+x+...+x+x)

and

2x = 1+1+1+1+...+1+1+1 (2x number of times)

Wah this discussion still going on arr... See the wiki site on the previous page la... While it's true that
x^2=x+x+x+x+...+x+x (x number of times)
and
d/dx(x^2)=2x,

the mistake is
d/dx(x+x+x+...+x+x)=1+1+1+1+...+1+1+1 (x number of times)
because x here is not held constant.

d/dx (x+x+...x+x) is in fact flawed. Remember that x increase at the magnitude of power of 2;
Let say x = 10
d/dx(x^2) = x+x+...x+x (10 times, with the value of x = 10)
Let say x = 11
d/dx(x^2) = x+x+...x+x (11 times, with the value of x = 11)
Why I say it is flawed, because the "x number of times" is not reflected in the equation, but only the value of x.

The true definition of d/dx is rate of change. For the equation y=x^2, the derivative (d/dx=2x) simply means the rate of change for the function when x is at certain value.

Let x = 10;
d/dx (x^2) = 2x = 20;

By rate of change, it means that any changes to the value, it is effectively scaled with that magnitude.

Say x = 10.001; the change (dx) = 0.001;
Effectively, the result should be = 10 + 0.001*20 = 10.02
Double check 10.001^2 = 10.020001