Question

find the second derivative of f(x)=3/(x^2+12)

Answer 1

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second derivative 3/(x^2+12)

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Answer 2

write it as
y = 3(x^2 + 12)^-1
y' = -3(x^2 + 12)^-2 (2x)
= -6x(x^2 + 12)^-2

y'' = (-6x)(-2)(x^2 + 12)^-3 (2x) - 6(x^2 + 12)^-2
= 24x^2 (x^2+12)^-3 - 6(x^2+12)^-2
= 6(x^2+12)^-3 [ 4x^2 - x^2 - 12]
= 6(x^2+12)^-3 [ 3x^2 -12]
= 18(x^2 -4)/(x^2 + 12)^3
or
18(x^2-4)/(x^2 + 12)^3

Answer 3

In the second derivative, second line, what happened to the -2 power on the end of the line. It looks like you just dropped it. I can't see where it was factored out.