How to Differentiate Complex Functions Using Product and Chain Rules?

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SUMMARY

The discussion focuses on differentiating complex functions using the product and chain rules. The first question involves differentiating the function f(x) = ax(2x + b)^7, where the product rule and chain rule are applied. The second question addresses the differentiation of f(x) = (x^2 + cos^3(x^4))^10, which requires the application of the chain rule twice. Participants confirm that breaking down the functions and systematically applying these differentiation rules simplifies the process.

PREREQUISITES
  • Understanding of the product rule in calculus
  • Knowledge of the chain rule in calculus
  • Familiarity with polynomial and trigonometric functions
  • Basic skills in function notation and differentiation
NEXT STEPS
  • Practice differentiating functions using the product rule
  • Explore advanced applications of the chain rule in calculus
  • Learn how to differentiate composite functions effectively
  • Review examples of differentiating trigonometric functions
USEFUL FOR

Students studying calculus, educators teaching differentiation techniques, and anyone looking to strengthen their understanding of advanced differentiation methods.

bonzy87
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Hi 2 questions having a mental block and can't figure them out any help would be apprieciated

Q1 differentiate f(x)=ax(2x+b)^7 where a and b are constants

Q2 differentiate f(x)=(x^2+cos^3(x^4))^10

thanks for any help cheers
 
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Hmmm...

Q1) Product rule, chain rule.

Q2) Chain rule, chain rule

Not too hard, really. Just break them up and apply the appropriate differentiation rules.
 

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