The derivative of sin(x)/x^2e^x?

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SUMMARY

The derivative of the function y=(sin(x))/(x^2e^x) is calculated using the quotient rule combined with the product rule. The quotient rule is applied first to differentiate the overall function, while the product rule is utilized specifically to differentiate the denominator, x^2e^x. This two-step approach ensures accurate differentiation by addressing the complexity of the denominator effectively.

PREREQUISITES
  • Understanding of calculus concepts, specifically differentiation
  • Familiarity with the quotient rule for derivatives
  • Knowledge of the product rule for derivatives
  • Basic trigonometric functions, particularly sine
NEXT STEPS
  • Practice applying the quotient rule with complex denominators
  • Study examples of using the product rule in conjunction with the quotient rule
  • Explore advanced differentiation techniques, such as implicit differentiation
  • Learn about Taylor series expansions for trigonometric functions
USEFUL FOR

Students studying calculus, mathematics educators, and anyone seeking to improve their skills in differentiation techniques.

dylanhouse
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I need to find the derivative of y=(sinx)/(x^2e^x)?

I tried using the product rule on the denominator and then I assume I need to use the quotient rule. But I'm not sure if I use the quotient rule with the derivative I found for the denominator or? I'm confused :$
 
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dylanhouse said:
I need to find the derivative of y=(sinx)/(x^2e^x)?

I tried using the product rule on the denominator and then I assume I need to use the quotient rule. But I'm not sure if I use the quotient rule with the derivative I found for the denominator or? I'm confused :$

You have the idea. You start differentiating with the quotient rule. In the process of doing that, at the part where you have to differentiate the denominator, right there use the product rule to differentiate the denominator, then continue. So you use the product rule in the middle of doing the quotient rule.
 

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