How to Differentiate the Function g(x) = (4+csc²(3x))²?

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Discussion Overview

The discussion revolves around the differentiation of the function g(x) = (4 + csc²(3x))². Participants are examining the application of the chain rule and clarifying the correct form of the function to differentiate.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents their differentiation attempt and questions whether they applied the chain rule correctly.
  • Another participant seeks clarification on whether the function is g(x) = (4 + csc²(3x))² or g(x) = (4 + csc²(3x))¹/², noting that this distinction affects the differentiation process.
  • A subsequent reply confirms that the original function was indeed the square root, suggesting that the differentiation should reflect that form.
  • Another participant corrects the first participant's differentiation approach, indicating that the derivative should involve a factor of 2 rather than 1/2, based on the correct interpretation of the function.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct form of the function to differentiate, leading to differing approaches in the differentiation process.

Contextual Notes

The discussion highlights potential confusion regarding the original function's notation, which may lead to different interpretations and differentiation outcomes.

cowgiljl
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g(x) = (4+csc^2(3x))^2

this is what i got
1/2(4+csc^2(3x))^-1/2 * d/dx (4+csc^2(3x)

g'(x) = 1/2(4+csc(3x))^-1/2 (1+cot3)
did i go about this correct to get the answer or did i mess it up at the diretive part?

joe
 
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Is the question g(x) = (4+csc^2(3x))^2 or g(x) = (4+csc^2(3x))^1/2?

This makes a difference when applying the chain rule.
 
g(x) = (4+csc^2(3x))^1/2?

it is this one it was orginally the squrt of 4+csc^2(3x) i just attempted to simplify it
 
Yeah, from your work g(x)=(4+csc^2(3x))^2 should be

g(x)=2(4+csc^2(3x))^1 * d/dx (4+csc^2(3x)) instead of
g(x)=1/2(4+csc^2(3x))^-1/2 * d/dx (4+csc^2(3x))

otherwise that last one would have corresponded an original equation written as g(x)=(4+csc^2(3x))^1/2
 

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