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posted by  jckst on 10/11/2008 9:51:18 PM  |  status: Live  

Derivative of a function

Course Textbook Chapter Problem
Calculus Calculus: Early Transcendentals (6th) by Stewart not from book 1
Question Details:
Hello Cramster world, I have a few questions I really need help with.  I have answered most of them, but am stuck of 3 of them that I just can't figure out.  This is the first one:
 
 .  Thanks for your help.  Jason
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posted by VietSpeed on 10/11/2008 9:58:54 PM  |  status: Live
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jckst's comment:
"Thanks for the help. You're quick. Jason"
Response Details:
f '(x) = use the quotient rule     d/dx(f(x)/(g(x))  = (g(x)f '(x) - f(x) g ' (x))/ (g(x))^2
but how did you end up with the denominator being squared? quotient rule
  g(x)     f '(x)  -     f(x)   g '(x) / ((g(x))^2
((x-4)(3x2+16)-(x3+16x)(1))/(x-4)^2       you got it Jason?

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posted by jckst on 10/11/2008 10:02:25 PM  |  status: Live
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Response Details:
Thanks for the speedy reply, but how did you end up with the denominator being squared?  Jason
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posted by Ctrl on 10/11/2008 10:09:46 PM  |  status: Live
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jckst's comment:
"Thank you for the excellent detail work. Jason"
Response Details:
Use the quotient rule for derivatives:


Let , then
let , then
and

Now put the pieces together:

= <----reduce doing basic algebra
= , or you could factor out a 2 at the numerator for the answer
= <---answer

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