How do I use the chain rule to differentiate this function?

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Homework Help Overview

The problem involves differentiating the function 2(x³ − 1)(3x² + 1)⁴ using the chain rule. Participants are exploring the application of differentiation rules in this context.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Some participants express uncertainty about using the chain rule and suggest that the product rule seems easier. There is a discussion about the differentiation steps taken, including attempts to apply both the product rule and chain rule.

Discussion Status

Participants are actively engaging with the problem, with some noting that the chain rule was inadvertently used in their attempts. There is a request for further clarification on how to properly apply the chain rule.

Contextual Notes

Some participants are referencing previous topics for additional context, indicating a continuity in their learning process. There is an acknowledgment of the complexity of the problem and the need for further assistance.

hadizainud
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Homework Statement



Differentiate the functions using chain rule. 2(x3 −1)(3x2 +1)4

Homework Equations



Chain Rule = f ' (g(x))g' (x)

The Attempt at a Solution



I don't know how to do using chain rule, but product rule is easier

So using product rule,

= f ' (x) g(x) + f (x)g' (x)
= (2)(x3-1)0(3x2)(3x2+1)4 + 2(x3-1)(4)(3x2+1)3(6x)
= (2)(3x2)(3x2+1)4 + 8(x3-1)(3x2+1)3(6x)

Can anyone show me how to do it, using chain rule?
 
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hadizainud said:

Homework Statement



Differentiate the functions using chain rule. 2(x3 −1)(3x2 +1)4

Homework Equations



Chain Rule = f ' (g(x))g' (x)

The Attempt at a Solution



I don't know how to do using chain rule, but product rule is easier

So using product rule,

= f ' (x) g(x) + f (x)g' (x)
= (2)(x3-1)0(3x[SUPdid]2[/SUP])(3x2+1)4 + 2(x3-1)(4)(3x2+1)3(6x)
= (2)(3x2)(3x2+1)4 + 8(x3-1)(3x2+1)3(6x)

Can anyone show me how to do it, using chain rule?
You did use the chain rule , along with the product rule.

You used the chain rule to differentiate (x3 −1) and (3x2 +1)4 !
 

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