Question

Find the derivative of $y=\frac{2x}{1-x^2}$

Answer 1

$y=\frac{2x}{1-x^2}$

here, $\frac{dy}{dx}=\frac{(1-x^2).2-2x(0-2x)}{(1-x^2{)}^2}$

$=\frac{2-2x^2+4x^2}{(1-x^2{)}^2}$ [Applying division Rule for differentiation]

$=\frac{2+2x^2}{(1-x^2{)}^2}$

$=\frac{2(1+x^2)}{(1-x^2{)}^2}$

So, here $\frac{dy}{dx}=\frac{2(1+x^2)}{(1-x^2{)}^2}$.