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Find the derivative of the following function

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data

    y = cos^3(5x^2-6)

    2. Relevant equations

    3. The attempt at a solution

    I used the chain rule for this question but im not sure about the cos^3 part. Using the chain rule i got


    But was I supposed to use the power rule on the cos^3 part? I can think of 3 ways this could be done but im not sure which way to go about it.

  2. jcsd
  3. Jan 25, 2009 #2
    You have to think of both cosine AND the exponent 3 as external functions. So you need to perform the chain rule twice:

    (d/dx) cos^3(5x^2-6) = 3 (cos(5x^2-6))^2 * (d/dx) cos(5x^2-6), at which you point you'll also need to do the chain rule cos(5x^2-6).
  4. Jan 25, 2009 #3
    How do I do the chain rule twice with this?

    I got 3 Cos(5x-6)^2 by -sin (5x^2-6)?

    Do I do something like ( 3 (-sin (5x^2-6) d/dx (5x^2-6))^2 ) (-sin (5x^2-6)

  5. Jan 25, 2009 #4
    I think I was making this too complicated.

    =d/dx Cos^3 d/dx (5x^2-6)
    =3Cos^2(5x^2-6) -sin(5x^2-6) 10x

    What do you guys an gals think?
  6. Jan 26, 2009 #5

    Gib Z

    User Avatar
    Homework Helper

    That is correct.
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