Derivative: sec4x tan4x + 8x/(1+x^4)

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Discussion Overview

The discussion revolves around the differentiation of the expression involving secant and arctangent functions, specifically the derivative of sec(4x) and the term 8x/(1+x^4). Participants are examining the application of the chain rule and the correct multiplication factors in the derivative calculation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a derivative expression but questions its correctness.
  • Another participant asks if the chain rule was applied correctly to the sec(4x) term.
  • A different participant points out a missing multiplication factor (du = 4) in the initial derivative calculation.
  • Further contributions suggest different forms of the derivative, with variations in the multiplication factors used.
  • One participant clarifies that only one factor of 4 should be retained in the derivative expression.
  • Another participant explains the differentiation process using the chain rule, confirming the derivative of sec(4x) as 4sec(4x)tan(4x).

Areas of Agreement / Disagreement

Participants express differing views on the correct application of the chain rule and the appropriate multiplication factors in the derivative, indicating that the discussion remains unresolved.

Contextual Notes

There are unresolved aspects regarding the application of the chain rule and the handling of constants in the differentiation process, which may depend on participants' interpretations of the derivative rules.

helpm3pl3ase
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(sec4x + 4arctanx^2)=

(sec4x)(tan4x) + (4)(1/1+x^4)(2x).. Did I derive this correctly??
 
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Did you use the chain rule on the sec(4x) term?
 
you forgot to multiply by [tex]du = 4[/tex] in the first term
 
(sec4x)(4)(tan4x)(4) + (4)(1/1+x^4)(2x)

or

16(sec4x)(tan4x) + (4)(1/1+x^4)(2x)??
 
or do i keep just 1 4?? like this..

(sec4x)(tan4x)(4) + (4)(1/1+x^4)(2x)
 
It would only be one four. Let sec(4x)=sec(u).

Then d(sec4x)/dx = d(secu)/dx = secu*tanu*du/dx

du/dx = 4, so

sec(4x)' = 4sec(4x)tan(4x)
 

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