A community for students.
Here's the question you clicked on:
 0 viewing
 2 years ago
I am having trouble understanding the solution to a particular problem. The problem is this:
Differentiate f(x)=ln(sin(x))  (x^43x)^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).
 2 years ago
I am having trouble understanding the solution to a particular problem. The problem is this: Differentiate f(x)=ln(sin(x))  (x^43x)^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).

This Question is Closed

Jelliot
 2 years ago
Best ResponseYou've already chosen the best response.1To 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. :)

KimJ
 2 years ago
Best ResponseYou've already chosen the best response.0Ahh. I thought about that, but thought 1/sin(x) was wrong.

Jelliot
 2 years ago
Best ResponseYou've already chosen the best response.1The 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)

KimJ
 2 years ago
Best ResponseYou've already chosen the best response.0Great. Thanks for clarifying!
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.