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First and Second Derivativesby mmajames
Tags: derivatives 
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#1
Mar612, 09:50 PM

P: 12

1. The problem statement, all variables and given/known data
Just trying to find the first and second derivatives. X^2/(X^216) 1+X/1X X^3(X2)^2 2. Relevant equations Quotient Rule/Power Rule/Chain Rule 3. The attempt at a solution 


#2
Mar612, 09:51 PM

P: 40

For the first one, what is the derivative of f(x)/g(x)? In general, not for this specific function.



#3
Mar612, 09:54 PM

P: 12

(g(x)*f'(x)f(x)*g'(x))/g(x)^2



#4
Mar612, 09:56 PM

P: 40

First and Second Derivatives
okay, so if f(x) = x^2 and g(x) = x^2, what is the derivative of f(x)/g(x)?



#5
Mar612, 10:06 PM

P: 12

f(x) = x^2 and g(x) = x^2
x^2/x^2 ((x^2)(2x)(2x)(x^2))/ (x^2)^2 


#6
Mar612, 10:30 PM

P: 40

I mistyped (that g(x) should have been g(x)=x^2  16 [not sure how I messed that one up]), but you seem to know what you're doing. What specific question do you have?



#7
Mar612, 10:35 PM

P: 12

I'm mostly having trouble with the second derivatives.



#8
Mar612, 11:10 PM

P: 40

What do you have so far? Where are you getting stuck?



#9
Mar812, 07:17 PM

P: 12

Well here's what I've got, I think they're right but I'm not sure.
f(x)=X^2/(x^216) (X^216)(2X)(X^2)(2X)/(X^216)^2 f'(x)=32X^2/(X^216)^2 (X^432X^2+256)(64X)(32X^2)(4X^364X)/(X^432X^2+256)^2 64x^5+2048X^316384X+128X^52048X^3 f''(x)=64X^516384X/(X^432X^2+256)^2 f(x)=1+x/1X (1X)(1)(1+X)(1)/(1X)^2 f'(x)=22X/(1X)^2 (X^22X+1)(2)(2X2)(22X)/(X^22X+1)^2 f''(x)=2X^2+4X+2/(X^22X+1)^2 f(x)=X^3(X2)^2 (X^3)(2X4)+(3X^2)(X2)^2 2X^44X^3+3X^412X^3+12X^2 f'(x)=5X^416X^3+12X^2 5X^416^3+12X^2 f''(x)=20X^348X^2+24X 


#10
Mar812, 09:09 PM

P: 12

Am I doing these correctly?



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