# Thread: Fundamental question: we know that y = x dy/dx, or rather... y/x = dy/dx...

1. ## Fundamental question: we know that y = x dy/dx, or rather... y/x = dy/dx...

I'm confused:
we know that y = x dy/dx, or rather... y/x = dy/dx,
suppose y = x^2,
dy/dx = 2x
y/x = 2x
y = (2x)x
y = 2x^2 ? contradiction?

2. Originally Posted by dinomight
I'm confused:
we know that y = x dy/dx, or rather... y/x = dy/dx,
suppose y = x^2,
dy/dx = 2x
y/x = 2x
y = (2x)x
y = 2x^2 ? contradiction?
Yes it is contradiction - and it says that:

y =x^2

is NOT a solution for:

y = x dy/dx ..... !

3. Originally Posted by dinomight
I'm confused:
we know that y = x dy/dx, or rather... y/x = dy/dx,...
Are you saying that you think this equality is true for all x and y?

4. Originally Posted by stapel
Are you saying that you think this equality is true for all x and y?
I think that the OP is saying just that. (To OP) Why do you think that equation is always true (called an identity)? YOU even found a counter example! You are thinking that y=dy and x=dx? If if y=x^2, then to compute the derivative, dy/dx, you just divide both sides by x? So there is no need to ever use the product rule, the quotient rule nor the chain rule since you can just divide by x? Please think about what I am saying!

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