1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    -10xSin^3(5x^2-6)

    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.

    Thanks!
     
  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
    =-30xCos^2(5x^2-6)Sin(5x^2-6)

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

    Gib Z

    User Avatar
    Homework Helper

    That is correct.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Find the derivative of the following function
Loading...