How to Approach Differentiating f(x) = (x^2 - x)sin(x)?

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SUMMARY

The discussion focuses on differentiating the function f(x) = (x² - x)sin(x) using calculus rules. Participants emphasize the importance of applying the product rule before the chain rule, clarifying that the product rule is essential for this function. The correct derivative is derived as f'(x) = (x² - x)cos(x) + sin(x)(2x - 1). This approach ensures accurate differentiation without unnecessary complexity.

PREREQUISITES
  • Understanding of the product rule in calculus
  • Familiarity with the chain rule in calculus
  • Knowledge of basic trigonometric functions, specifically sine and cosine
  • Ability to manipulate polynomial expressions
NEXT STEPS
  • Study the application of the product rule in calculus
  • Review examples of differentiating trigonometric functions
  • Practice problems involving the chain rule and product rule
  • Explore advanced differentiation techniques, such as implicit differentiation
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Students studying calculus, mathematics educators, and anyone seeking to improve their skills in differentiating complex functions involving trigonometric and polynomial expressions.

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Homework Statement


f(x)=(x2-x)(sin(x))

Homework Equations


Chain rule
Product rule

The Attempt at a Solution


f'g(x)*g'(x)
cosx

(2x-x)(cosx)

Would you use the product rule after using the power rule and chain rule?
 
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Review the product rule !
 
Joyci116 said:

Homework Statement


f(x)=(x2-x)(sin(x))


Homework Equations


Chain rule
Product rule


The Attempt at a Solution


f'g(x)*g'(x)
cosx
?
This looks like you're attempting to use the chain rule.
Joyci116 said:
(2x-x)(cosx)

Would you use the product rule after using the power rule and chain rule?
No. Use the product rule first. You don't need the chain rule at all.
 
(x2-x)cosx+sinx(2x-1)

X2cosx-xcosx+2xsinx-sinx
 
That's more like it!
 

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