Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

aprilanahi

  • 2 years ago

find the derivative of sin[ln(cosx^3)]

  • This Question is Closed
  1. sweet1137
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    chain rule 3 times. lol

  2. Directrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    In sin[ln(cosx^3)] is (cosx^3) meant to be (cos(x)) ^3 OR is it meant to be ( cos(x^3) ) ? They are not the same.

  3. aprilanahi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cos(x^3)

  4. sweet1137
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    here: we start by taking the derivative of the outside function sin(u) where u = ln(cosx^3). This is equal to cos(u)*du/dx. Then, du/dx requires the use of the chain rule again, therefore du/dx = d/dx ln(v) where v = cos(x^3). This is equal to (1/v)*dv/dx. We have that dv/dx requires use of the chain rule as well, so dv/dx = d/dx cos(k) where k = x^3. This is equal to -sin(k)*3x^2. So the final answer all together is: cos(ln(cosx^3))*(1/cosx^3)*(-sin(x^3))*3x^2

  5. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.