Don't follow one small step in proof

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SUMMARY

The discussion centers on the application of the chain rule in calculus, specifically in the proof for the derivative of arcsin(x). The transition from d/dx sin(y) to dy/dx cos(y) illustrates the chain rule's function of differentiating composite functions. Participants clarify that recognizing the function as sin(y(x)) makes the application of the chain rule evident. This highlights the importance of understanding derivative proofs in calculus.

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  • Understanding of basic calculus concepts, particularly derivatives
  • Familiarity with the chain rule in differentiation
  • Knowledge of inverse trigonometric functions, specifically arcsin
  • Ability to interpret mathematical notation and proofs
NEXT STEPS
  • Study the chain rule in depth, focusing on its applications in composite functions
  • Review proofs for derivatives of other inverse trigonometric functions, such as arccos and arctan
  • Practice solving derivative problems involving implicit differentiation
  • Explore advanced calculus topics, including higher-order derivatives and their proofs
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Students of calculus, mathematics educators, and anyone seeking to deepen their understanding of derivative proofs and the application of the chain rule.

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andrewkirk said:
It is applying the rule for derivative of a function of a function. This is more apparent if we write it as ##\frac d{dx}\sin(y(x)) ##.
So it's just the chain rule. Can't believe I missed that. Thanks for your help!
 

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