Differentiation Ax^b with f(x) already given

[jameswill1am]

Homework Statement

The function f is defined as f(x)=x^4, then;

f'(3x^3)=?

d[f(3x^3)]/dx=?

f'(xy^3)=?

Homework Equations

The Attempt at a Solution

My problem here is not so much doing the differentiation itself but understanding the notation.

1. for f'(3x^3) i want to differentiate my f(x) to get 4x^3 and then f'(3x^3)=4(3x^3)^3?

2. Here i want to diff. (3x^3)^4?

3. And for the third i want to put f'(xy^3)is equal to f'(x) and then put in x=(xy^3), and so something like 4(xy^3)^3?

Let me know if I'm on the right tracks. cheers

 

[Mark44]

First you'll need f'(x). Then you need to evaluate that function at 3x³.

As an example, suppose that g(x) = x³ and you want g'(2x²).

g'(x) = 3x², so g'(2x²) = 3(2x²)² = 3 * 4x⁴ = 12x⁴.
Edit: Never mind. It looks like you have the idea.
2. That looks right.
3. Looks right.

 

[jameswill1am]

Thanks i felt as though i new what i was doing but hours without sleep had caused me to doubt myself. Thanks for the concise reply and for the peace of mind.