Let f(x)=ln(x2+1x2−13)f(x) = \ln(\sqrt[3]{\frac{x^2+1}{x^2-1}})f(x)=ln(3x2−1x2+1). Determine f′(x)f'(x)f′(x).
2x3(x4−1)\frac{2x}{3(x^4-1)}3(x4−1)2x
−4x3(x4−1)\frac{-4x}{3(x^4-1)}3(x4−1)−4x
2x3(x2+1)(x2−1)\frac{2x}{3(x^2+1)(x^2-1)}3(x2+1)(x2−1)2x
−4x3(x2+1)(x2−1)\frac{-4x}{3(x^2+1)(x^2-1)}3(x2+1)(x2−1)−4x