Question

Differentiate : $f\left(x\right)=\sqrt{\frac{1+x^2}{1-x^2}}$

Answer 1

$f\left(x\right)=\sqrt{\frac{1+x^2}{1-x^2}}{f}^1\left(x\right)=\frac{\frac{2x(1-x^2)+2x(1+x^2)}{(1-x^2{)}^2}}{2\sqrt{\frac{1+x^2}{1-x^2}}}\frac{4x}{(1-x^2{)}^2}\times \frac{\sqrt{1-x^2}}{2\sqrt{1+x^2}}=\frac{2x}{(1-x^2{)}^{3/2}\sqrt{1+x^2}}$