Question

Let $f\left(x\right)=\frac{x^2}{1-x^2},x\ne 0,\pm 1$, then derivative of $f\left(x\right)$ with respect to $x$, is

• A. $\frac{2x}{(1-x^2{)}^2}$
• B. $\frac{1}{(1+x^2{)}^3}$
• C. $\frac{1}{(1-x^2{)}^2}$
• D. $\frac{1}{(2-x^2{)}^2}$

Answer 1

Answer: (A)

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

$f\left(x\right)=\frac{x^2}{1-x^2};x\ne 0,\pm 1$

$f^{\prime }\left(x\right)=\frac{(1-x^2)\frac{d}{dx}{x}^2-x^2\frac{d}{dx}(1-x^2)}{(1-x^2{)}^2}$

$f^{\prime }\left(x\right)=\frac{(1-x^2).2x-x^2.(-2x)}{(1-x^2{)}^2}$

$f^{\prime }\left(x\right)=\frac{2x-2x^3+2x^3}{(1-x^2{)}^2}$

$f^{\prime }\left(x\right)=\frac{2x}{(1-x^2{)}^2}$

$\therefore f^1\left(x\right)=\frac{2x}{(1-x^2{)}^2}$