posted by Haley on .
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?
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