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)

u should look at it this way:

d/dx(x) = 1
d/dx(x+x) = 1+1
d/dx(x+x+x)=1+1+1
...
d/dx(x+x+x+...+x [y number of times])=1+1+1+...+1 [y number of times]

d/dx(yx)=1+1+1+...+1 [y number of times]
d/dx(yx)=y

use y as a factor instead of x, so it won't affect the differentiation in terms of x.

I guess, to really understand this, u gotta search deep into the Differentiation from First Principle

This post has been edited by loongchai: Jul 16 2009, 01:49 AM

y is a factor.

y cannot be x because it causes the line of the graph to be different.

Differentiation is derived from graphs.


For example,

From the straight line equation, y=mx+c,

dy/dx is the slope of the graph or m.

If you were to replace m with x, the graph would not be linear anymore. (y = x^2 + c) You would be changing the linear line to a curve.

In this case, m is a factor. Same goes to y from the TS's question.

I am not very good at explaining.

No, of course we can differentiate more than a linear graph. If you were to add a x factor to a linear function, it turns to a curve. And if you were to add another x to the curve function, it becomes another type of graph. And it goes on. However, adding a factor instead of x would only change the scale of the graph.

This post has been edited by loongchai: Jul 16 2009, 06:15 PM

The original problem will only happen if we were to equate y to x or y=x. I am trying to prove that y cannot be equal to x. This is because if y=x, then the graph will be different, which affects the differentiation. y, being a factor will only affect the scale of the graph, not the shape of it.

You are making things complicated...

y can never be equal to x? That only applies to the original question.



This post has been edited by loongchai: Jul 16 2009, 11:25 PM