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What is the second derivative of (x^3)/(x^2-1)? And how would I accurately graph both the derivative and the second derivative of this function?

1 answer

Just do a web search for online graphing calculators. There are bunches.

y = x3/(x2-1)

y' = [3x2 * (x2-1) - x3 * 2x]/(x2-1)2
= (x4 - 3x2)/(x2-1)2

y'' = [(4x3 - 6x)(x^2-1)2 - (x4 - 3x2)*2*(x2-1)*2x]/(x2-1)4
= (2x3 + 6x)/(x2-1)3
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