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Differentiation Ax^b with f(x) already given

  1. Oct 6, 2009 #1
    1. The problem statement, all variables and given/known data

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

    f'(3x^3)=?

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

    f'(xy^3)=?

    2. Relevant equations



    3. 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
     
  2. jcsd
  3. Oct 6, 2009 #2

    Mark44

    Staff: Mentor

    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.
     
    Last edited: Oct 6, 2009
  4. Oct 6, 2009 #3
    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.
     
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