Graph of a trigonometric function

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SUMMARY

The discussion focuses on graphing the derivative of the function f(x) = sin(x + sin(2x)) over the interval 0 ≤ x ≤ π. The derivative is calculated using the chain rule, resulting in f'(x) = (1 + 2cos(2x))cos(x + sin(2x)). Participants seek guidance on the next steps for graphing this derivative function effectively.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Knowledge of calculus, specifically the chain rule for differentiation
  • Familiarity with graphing techniques for functions
  • Experience with graphing software or tools
NEXT STEPS
  • Learn how to graph trigonometric functions using software like Desmos or GeoGebra
  • Study the implications of the derivative on the shape of the graph
  • Explore the behavior of f'(x) = (1 + 2cos(2x))cos(x + sin(2x)) over the specified interval
  • Investigate the critical points and inflection points of the function f(x)
USEFUL FOR

Students and educators in mathematics, particularly those studying calculus and trigonometry, as well as anyone interested in visualizing the behavior of complex functions and their derivatives.

Duane
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How do you graph f'(x) when f(x)= sin(x+sin2x), 0≤x≤∏ ?

If I calculate f'(x) first by the chain rule, I get f'(x)=cos(x+sin2x)(1+cos2x), where to proceed ?

Thanks for any help in advance.
 
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Duane said:
How do you graph f'(x) when f(x)= sin(x+sin2x), 0≤x≤∏ ?

If I calculate f'(x) first by the chain rule, I get f'(x)=cos(x+sin2x)(1+cos2x), where to proceed ?

Thanks for any help in advance.

Do not forget the '2'.

f'(x)=(1+2cos2x)cos(x+sin2x)
 
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