Combining product rule with chain rule

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SUMMARY

The derivative of the function y = x² sec(x - 5) is found by applying the product rule in conjunction with the chain rule. The product rule is utilized to differentiate the product of x² and sec(x - 5), while the chain rule is applied to differentiate sec(x - 5) where (x - 5) is the inner function. This method ensures accurate differentiation of composite functions.

PREREQUISITES
  • Understanding of the product rule in calculus
  • Knowledge of the chain rule in calculus
  • Familiarity with trigonometric functions, specifically secant
  • Basic differentiation techniques
NEXT STEPS
  • Practice applying the product rule with various functions
  • Study the chain rule in more complex scenarios
  • Explore differentiation of trigonometric functions
  • Learn about higher-order derivatives and their applications
USEFUL FOR

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

ziddy83
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Hey what's up,
The problem is...find the derivative of:

y= x^2 sec(x-5)

My question is...Would I start off by using the product rule and combine the chain rule with it, with x-5 being the inner function and sec(u) being the outer function? thanks...
 
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That is correct, use the product rule then the chain-rule.
 
ok.. thanks a lot
 

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