A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Differentiate a func with wrt another ? f(x) = arcsin((2x)/(1+x^2)) and g(x) = arccos((1x^2)/(1+x^2)) , then df(x)/dg(x) = ?
How do I do this ? df(x)/dx * dx/dg(x) ?
anonymous
 5 years ago
Differentiate a func with wrt another ? f(x) = arcsin((2x)/(1+x^2)) and g(x) = arccos((1x^2)/(1+x^2)) , then df(x)/dg(x) = ? How do I do this ? df(x)/dx * dx/dg(x) ?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=\sin ^{1} ( (2x) / (1+x^2) ) \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[g(x)=\cos ^{1} ( (1x^2) / (1+x^2) ) \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I worked it out as http://www.wolframalpha.com/input/?i=derivative+of+arcsin%28%282x%29%2F%281%2Bx^2%29%29+*+%281%2F+derivative+of+arccos%28%281x^2%29%2F%281%2Bx^2%29%29%29

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but seems to lengthy to do. :( ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0df(x)/dx=2/(1+x^2) and dg(x)/dx=2/(1+x^2) dx/dg(x)=(1+x^2)/2 so df(x)/dg(x)=1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0akanksha: what you mentioned before is right, but (df(x)/dx)/ (dg(x)/dx) would be a better choice!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok right, you did the same thing. There is no other way to do it! :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0@Abdul , how did y ou do that ??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0OK, you have another way to do it. \[x = \tan \theta\] Thus \[f(x) = \sin^{1}\sin(2 \theta)\]\[= 2 \theta\] \[g(x) = \cos^{1} \cos(2 \theta)\]\[= 2 \theta\] so the answer is 1.
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.