Other ways of expressing a derivative.

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Discussion Overview

The discussion revolves around alternative expressions for the derivative of the function x², specifically focusing on the relationship between the derivative and the variable y. Participants explore the implications of expressing the derivative in terms of y and its connection to the rate of change of the function.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions how the derivative 2x relates to y, expressing confusion over the absence of a y component in the derivative expression.
  • Another participant states that if y = x², then dy/dx = 2x, indicating a standard interpretation of the derivative.
  • A later reply reiterates the confusion about the relationship between y and 2x, suggesting that 2x represents the instantaneous rate of change of y at a given x.
  • One participant proposes an alternative expression, dy/dx = 2√y, although they express uncertainty about the relevance of this to the original question.
  • Another participant emphasizes that at any point x, the slope of the curve y = x² is equal to 2x, reinforcing the connection between the derivative and the curve's behavior.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the relationship between the derivative and y, with no consensus reached on how to express the derivative in a way that incorporates y.

Contextual Notes

Some assumptions about the relationship between x and y may be implicit, and the discussion does not resolve the connection between the derivative and the variable y in a definitive manner.

jasonlr82794
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Hey, I was wondering if there is another way of expressing the derivative 2x(the derivative of the function x^2). I was wondering because there doesn't seem to be a y part to this. Like in y/x, a change in x makes a change in y. So how would I express this with y as well?
 
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If y = x^2, then dy/dx = 2x.
 
Yeah, I know, but what does the y have to do with the 2x?
 
jasonlr82794 said:
Yeah, I know, but what does the y have to do with the 2x?
If ##y=x^2##, then 2x is the instantaneous rate of change of y at x.
 
dy/dx=2√y ? not exactly sure what you're asking..
 
jasonlr82794 said:
Yeah, I know, but what does the y have to do with the 2x?
At any point x, the slope of the y=x2 curve is known and is equal to 2x.
 

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