Calculate f'(x) given d/dx(f(3x^4))=6x^4?

[firegoalie33]

I am told that d/dx(f(3x^4))=6x^4. I need to calculate f ' (x). i have tried like 3 different methods and have no idea how to do this.
Help please!

 

[Office_Shredder]

Can you find f'(3x⁴)?

 

[HallsofIvy]

By the chain rule,
$$\frac{df(3x^4)}{dx}= f'(3x^4)(12x^3)$$

So you must have $f'(3x^4)(12x^3)= 6x^4$.

That let's you find $f'(3x^4)$ per Office Shredder's question. Now, if you let $u= 3x^4$, you can find f'(u).