First and Second Derivatives

by mmajames
Tags: derivatives
 P: 12 1. The problem statement, all variables and given/known data Just trying to find the first and second derivatives. X^2/(X^2-16) 1+X/1-X X^3(X-2)^2 2. Relevant equations Quotient Rule/Power Rule/Chain Rule 3. The attempt at a solution
 P: 40 For the first one, what is the derivative of f(x)/g(x)? In general, not for this specific function.
 P: 12 (g(x)*f'(x)-f(x)*g'(x))/g(x)^2
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)?
 P: 12 f(x) = x^2 and g(x) = x^-2 x^2/x^-2 ((x^-2)(2x)-(-2x)(x^2))/ (x^2)^2
 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?
 P: 12 I'm mostly having trouble with the second derivatives.
 P: 40 What do you have so far? Where are you getting stuck?
 P: 12 Well here's what I've got, I think they're right but I'm not sure. f(x)=X^2/(x^2-16) (X^2-16)(2X)-(X^2)(2X)/(X^2-16)^2 f'(x)=-32X^2/(X^2-16)^2 (X^4-32X^2+256)(-64X)-(-32X^2)(4X^3-64X)/(X^4-32X^2+256)^2 -64x^5+2048X^3-16384X+128X^5-2048X^3 f''(x)=64X^5-16384X/(X^4-32X^2+256)^2 f(x)=1+x/1-X (1-X)(1)-(1+X)(-1)/(1-X)^2 f'(x)=2-2X/(1-X)^2 (X^2-2X+1)(-2)-(2X-2)(2-2X)/(X^2-2X+1)^2 f''(x)=2X^2+4X+2/(X^2-2X+1)^2 f(x)=X^3(X-2)^2 (X^3)(2X-4)+(3X^2)(X-2)^2 2X^4-4X^3+3X^4-12X^3+12X^2 f'(x)=5X^4-16X^3+12X^2 5X^4-16^3+12X^2 f''(x)=20X^3-48X^2+24X
 P: 12 Am I doing these correctly?

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