Solve for the Derivative of Inverse Function g

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SUMMARY

The discussion focuses on finding the derivative of the inverse function g, defined as g = 1/(f-1). Given that f(6) = 18 and f'(6) = 4/5, participants emphasize the importance of understanding the theorem related to derivatives of inverse functions. The key takeaway is to apply the inverse function theorem to compute g'(18) effectively.

PREREQUISITES
  • Understanding of inverse functions and their properties
  • Familiarity with the inverse function theorem
  • Basic knowledge of derivatives and differentiation techniques
  • Ability to interpret function notation and notation for derivatives
NEXT STEPS
  • Review the inverse function theorem in calculus textbooks
  • Practice problems involving derivatives of inverse functions
  • Learn how to apply the chain rule in the context of inverse functions
  • Explore examples of calculating derivatives for various types of functions
USEFUL FOR

Students studying calculus, particularly those focusing on derivatives and inverse functions, as well as educators seeking to reinforce these concepts in their teaching materials.

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Homework Statement


Suppose that f has an inverse and f (6) = 18, f'(6) = 4/5. If g = 1/(f-1), what is g'(18)?

have no idea how to set up problem
 
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Do you read your textbook at all? If not then you should! In it you'll find a theorem that specifically deals with derivatives of inverse functions. Please flip through the section in which this exercise occurs and see if you can't find it. Then we can get started.
 

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