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

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Homework Help Overview

The discussion revolves around differentiating the function f(x) = (x^2 - x)sin(x), focusing on the application of differentiation rules such as the product rule and chain rule.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the appropriate differentiation techniques, particularly whether to apply the product rule or chain rule first. There is an exploration of the initial attempts at differentiation and the correctness of those attempts.

Discussion Status

Some participants have provided feedback on the differentiation approach, suggesting a preference for using the product rule first. There is an ongoing examination of the steps involved in the differentiation process, with varying interpretations of the rules to apply.

Contextual Notes

Participants reference specific differentiation rules and express uncertainty about the sequence of applying these rules. There is a focus on ensuring the correct application of the product rule in the context of the given function.

Joyci116
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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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