Cramster.com - Homework Solutions, Lecture Notes, Exams, and Free Online Homework Help
Sign Up Now! Login Customer Support Cramster Blog
McAfee Secure sites help keep you safe from identity theft, credit card fraud, spyware, spam, viruses and online scams
Problem Solved.
    Home    
    Homework Help    
   Answer Board   
    Resources (Beta)    
   
You Are Here: Home > Answer Board > Calculus > Topic: Easy Derivative 5 - I Rate Lifesaver Points
Member's Topic Headline:

Easy Derivative 5 - I Rate Lifesaver Points

Know the answer? Have a better solution? Share it.
Sign Up Now for FREE!
Join the thousands of students
getting ahead in their classes.
Member Testimonials

Question:

Advertisement:
Answer | Ask New Question | Customize Profile | Leaderboards | 
FAQ

Member's Avatar
Sage
Karma Points: 3,348
Respect (98%):
Date Posted: 7/23/2008 2:10:11 AM  Status: Closed
Easy Derivative 5 - I Rate Lifesaver Points
Course Textbook Chapter Problem
Calculus N/A N/A N/A
Question Details:
Find the derivative.
y = (x^2+1)^10 sqrt(x^4+9)
Bonus Point Alert! Earn +4 additional karma points for helping this annual member.
Please take one moment to rate my response - I would really appreciate it! =)

Answers:

Member's Avatar
Scholar
Karma Points: 219
Date Posted: 7/23/2008 2:46:09 AM  Status: Live
Asker's Rating: Helpful   
Response:
recall: y' = f'(x)g(x) + f(x)g'(x)
 
f(x) = (x2 + 1)10
f'(x) = 10(x2 + 1)9 * (2x)   by the chain rule
g(x) = √(x4 + 9)
g'(x) = 1/2(x4 + 9)-1/2 * (4x3)   by the chain rule
 
Therefore:
y' = 10(x2 + 1)9(2x)√(x4 + 9) + (x2 + 1)101/2(x4 + 9)-1/2(4x3)
 
Simplify:
y' = 20x(x2 + 1)9√(x4 + 9) + (4x3(x2 + 1)10) / (2√(x4 + 9))
 
I hope this helps.
 
Good luck!

Member's Avatar
Rookie
Karma Points: 7
Date Posted: 7/23/2008 3:33:50 AM  Status: Live
Asker's Rating: Helpful   
Response:
Let  f(x) = (x2 + 1)10  and p(x) = √(x4+9) = (x4 + 9)1/2
 
∴y = f(x).p(x)
so the derivative of y can be written as
dy/dx = d/dx ( f(x).P(x) )
          = p(x). df(x)/dx + f(x).dp(x)/dx
      y' = p(x).f '(x) + f(x).p'(x)
      y' = (x4+9)1/2 .10(x2+1)9 .2x + (x2+1)10 .(1/2)(x4+9)-1/2.4x3
         = 20x(x4+9)1/2 (x2+1)9 +  2x3. (x2+1)10(x4+9)-1/2
  ∴y' = 2x(x2+1)9 {10(x4+9)1/2 + x2(x2+1)(x4+9)-1/2}

Member's Avatar
Sage
Karma Points: 4,678
Date Posted: 7/23/2008 1:53:47 PM  Status: Live
Asker's Rating: Helpful   
Response:
Hi,

For this question, we need to use the Product Rule which states the following:



Next, let's define these terms to get:

u =             u' =

v =           v' = =

Now, let's apply the Product Rule which I typed out at the beginning of the posting to get:

+= y'

I hope that helps you out!  Please let me know if you have any other questions! =)
The VC
-----
The people who don't mind matter and the people who mind don't matter. -Real World Denver Quote
------
Math Tutor
 

Member's Avatar
Oracle
Karma Points: 54,611
Date Posted: 7/23/2008 2:06:05 PM  Status: Live
Asker's Rating: Helpful   
Response:
 
 
 
 
 
 
 

 

Member's Avatar
Sage
Karma Points: 3,348
Date Posted: 7/23/2008 11:03:06 PM  Status: Live
Asker's Rating: N/A-Posted by Person Asking Question   
Response:
The answer was:

2(x2+1)9 (21x2 - 30x + 1)

Thanks for the help.
Please take one moment to rate my response - I would really appreciate it! =)



By reading or posting messages on these forums, you are agreeing to the Answer Board's Terms of Service and Conduct (TSC).


About Cramster | Terms of Use | Privacy Policy | Contact Us | Press Room | Site Map | Support | Anti-Cheating Policy

Cramster.com is not affiliated with any publisher. Book covers, title and author names appear for reference only.
Copyright © 2008 Cramster, Inc.