[tex]f'(x)= \frac{1}{2 \sqrt{ \frac{x^2-2}{x^2+1} } } \cdot( \frac{x^2-2}{x^2+1})'\\
f'(x)= \frac{1}{2} \sqrt{ \frac{x^2+1}{x^2-2} } \cdot \frac{2x(x^2+1)-2x(x^2-2)}{(x^2+1)^2} \\
f'(x)=\frac{1}{2} \sqrt{ \frac{x^2+1}{x^2-2} } \cdot \frac{2x(x^2+1-x^2+2)}{(x^2+1)^2} \\
f'(x)=\frac{1}{2} \sqrt{ \frac{x^2+1}{x^2-2} } \cdot \frac{6x}{(x^2+1)^2} \\
f'(x)=\sqrt{ \frac{x^2+1}{x^2-2} } \cdot \frac{3x}{(x^2+1)^2} [/tex]
