Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

KimJ

I am having trouble understanding the solution to a particular problem. The problem is this: Differentiate f(x)=ln(sin(x)) - (x^4-3x)^10. I can differentiate the second part of the function, but I dont quite understand differentiating the first part. I want to write (1/x)(sin(x))(cos(x)), but the solution says that it is cos(x)/(sinx(x).

  • one year ago
  • one year ago

  • This Question is Closed
  1. Jelliot
    Best Response
    You've already chosen the best response.
    Medals 1

    To differentiate the first part, you must use the chain rule. \[d/dx[\ln(\sin(x))]=(1/\sin(x))*\cos(x)=cot(x)\] Then, you just add the derivative of the first part to the derivative of the second part. :)

    • one year ago
  2. KimJ
    Best Response
    You've already chosen the best response.
    Medals 0

    Ahh. I thought about that, but thought 1/sin(x) was wrong.

    • one year ago
  3. Jelliot
    Best Response
    You've already chosen the best response.
    Medals 1

    The reason why the derivative of ln(sin(x)) is cos(x)/sin(x) instead of (1/x)*(1/sin(x))*cos(x) is that when you differentiate the natural log, it turns into 1/(whatever what inside) not just 1/x times 1/(whatever was inside)

    • one year ago
  4. KimJ
    Best Response
    You've already chosen the best response.
    Medals 0

    Great. Thanks for clarifying!

    • one year ago
  5. Jelliot
    Best Response
    You've already chosen the best response.
    Medals 1

    no problem :)

    • one year ago
    • Attachments:

See more questions >>>

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.