3.58: Differentiate $\left(\dfrac{x^{2} - 1}{x^{2} + 1}\right)^{4}$

Show that $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ can be written as $\dfrac{Ax(x^{2} - 1)^{3}}{(x^{2} + 1)^{5}}$, where $A$ is a positive integer to be found.

Show that the curve has stationary points where $x = -1$, $x = 0$ and $x = 1$.

Use the first derivative test to determine which two stationary points have the same nature and state whether they are maximum or minimum points.