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

[hadizainud]

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?

 

[SammyS]

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 !

 

[hadizainud]

Thanks! I don't realize that part.
I need your help on my previous topic.
Please do help me :)
https://www.physicsforums.com/showthread.php?t=559855

 

[SammyS]

I need your help on my previous topic.
Please do help me :)
https://www.physicsforums.com/showthread.php?t=559855

Looks like Mark44 and Dick have it covered !