What's the derivative of {sqrt (2x)} ?

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Discussion Overview

The discussion revolves around finding the derivative of the function √(2x). Participants explore different methods and rules for differentiation, including the power rule and the potential necessity of the chain rule.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant suggests that the derivative can be found without using the product rule, chain rule, or quotient rule, asking for a demonstration of the workings.
  • Another participant argues that the chain rule is necessary due to the presence of the "2" in the expression, providing a detailed calculation using the power rule.
  • A different viewpoint presents the expression as √2 √x, implying that this form can simplify the differentiation process using the power rule and scalar multiple rule.
  • Some participants express a light-hearted tone regarding the disagreement, indicating a playful debate among them.
  • Another participant humorously questions the sanity of the previous claims, suggesting a strong disagreement on the methods discussed.
  • One participant reiterates the expression in a different notation, again indicating a preference for using the power rule and scalar multiple rule.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the derivative can be found without the chain rule. Multiple competing views on the necessity of different differentiation rules remain present throughout the discussion.

Contextual Notes

Some participants rely on specific interpretations of differentiation rules, and there is an underlying assumption about the familiarity with these rules. The discussion does not resolve the mathematical steps or the applicability of the rules mentioned.

urbantrained
I'm told that you don't need the product rule, or chain rule, or quotient rule to work it out. Can anyone show the workings as well please...?
 
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I don't see anyway to find the derivative of √(2x) without using the chain rule (because of the "2", not the "√").

Write f(x)= (2x)1/2 and use the "power" rule:

f'(x)= (1/2)(2x)1/2-1(2x)'
= (1/2)(2x)-1/2(2)
= 1/√(2x)
 
√(2x) = √2 √x

You can take it from here using the power rule and the scalar multiple rule.
 
I love when you to Alfred E. Newmans fight it out.

- Warren
 
You must be mad!
 
Hurkyl
ã(2x) = ã2 ãx

You can take it from here using the power rule and the scalar multiple rule.

Oh, well, if want to do it the EASY way!
 

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