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

Click For Summary
SUMMARY

The discussion focuses on differentiating the function g(x) = (4 + csc²(3x))² using the chain rule. The initial attempt by the user involved applying the derivative incorrectly, leading to confusion about whether the function was originally g(x) = (4 + csc²(3x))² or g(x) = (4 + csc²(3x))¹/². The correct differentiation should utilize g'(x) = 2(4 + csc²(3x))¹ * d/dx(4 + csc²(3x)), ensuring proper application of the chain rule.

PREREQUISITES
  • Understanding of calculus, specifically differentiation techniques
  • Familiarity with the chain rule in calculus
  • Knowledge of trigonometric functions, particularly cosecant and cotangent
  • Ability to manipulate and simplify algebraic expressions
NEXT STEPS
  • Study the chain rule in calculus with examples involving composite functions
  • Learn about the derivatives of trigonometric functions, including csc and cot
  • Practice differentiating complex functions with multiple layers of composition
  • Explore applications of derivatives in real-world scenarios, such as physics or engineering problems
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus, as well as educators teaching differentiation techniques and trigonometric derivatives.

cowgiljl
Messages
63
Reaction score
1
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
 
Physics news on Phys.org
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
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
6
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 27 ·
Replies
27
Views
4K