Solving Derivatives: A Puzzling Experience

[vanmaiden]

Homework Statement

I was messing around online when I found this: $\frac{dy}{2}$ = 2x. This was derived from the function y = x². I had never really seen anything like this before. When I solved for "dy," I got 4x. However, for example, when x changes from 0 to 2, the y changes from 0 to 4. Interestingly enough, "dy" is represented as being 4x and not just 4. Can someone point out what I did wrong?

Homework Equations

y = x²
$\frac{dy}{2}$ = 2x

The Attempt at a Solution

Pretty much explained in the "problem statement" by accident.

 

[SteamKing]

You find a lot of things on the internet. Shockingly, not all of them are true.

 

[vanmaiden]

You find a lot of things on the internet. Shockingly, not all of them are true.

That is true without a doubt! lol. How would I go about solving something like this though? I am given delta x and the derivative and have to find delta y. It all seems very interesting.

 

[HallsofIvy]

You wouldn't. The equation is meaningless. You cannot have a "dy" without a corresponding "dx". In terms of "non-standard analysis", we would say that the left side of the equation is an infinitesmal while the right side is not. That can't happen.

Since you say "This was derived from the function $y = x^2$" I suspect that it was supposed to be
$$\frac{dy}{dx}= x^2$$

 

[Mark44]

Homework Statement

I was messing around online when I found this: $\frac{dy}{2}$ = 2x. This was derived from the function y = x². I had never really seen anything like this before. When I solved for "dy," I got 4x. However, for example, when x changes from 0 to 2, the y changes from 0 to 4. Interestingly enough, "dy" is represented as being 4x and not just 4. Can someone point out what I did wrong?

Homework Equations

y = x²
$\frac{dy}{2}$ = 2x

The equation above should be dy = 2x dx

The Attempt at a Solution

Pretty much explained in the "problem statement" by accident.

 

[stallionx]

Homework Statement

I was messing around online when I found this: $\frac{dy}{2}$ = 2x. This was derived from the function y = x². I had never really seen anything like this before. When I solved for "dy," I got 4x. However, for example, when x changes from 0 to 2, the y changes from 0 to 4. Interestingly enough, "dy" is represented as being 4x and not just 4. Can someone point out what I did wrong?

Homework Equations

y = x²
$\frac{dy}{2}$ = 2x

The Attempt at a Solution

Pretty much explained in the "problem statement" by accident.

Here the point is, in my personal opinion

dy = 4*x

x is a variable but as the problem ( lamely presented ) offers

dy=0

and

thus
x=4*0

x=0 alwyas no matter what

Either wrongly presented or gives us the line equation

x = 0

 

[vanmaiden]

Here the point is, in my personal opinion

dy = 4*x

x is a variable but as the problem ( lamely presented ) offers

dy=0

and

thus
x=4*0

x=0 alwyas no matter what

Either wrongly presented or gives us the line equation

x = 0

Thank you

 

[stallionx]

Thank you

You are quite Welcome :)

 

[Mark44]

Here the point is, in my personal opinion

dy = 4*x

As HallsOfIvy already pointed out, this equation is meaningless, so there is not much point in analyzing it further.

x is a variable but as the problem ( lamely presented ) offers

dy=0

and

thus
x=4*0

x=0 alwyas no matter what

Either wrongly presented or gives us the line equation

x = 0