Question

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?

Answer 1

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