Question

Differentiate with respect to $x$

$\left[\frac{x^2}{x^2+1}\right]$

Answer 1

Let $y=\frac{x^2}{x^2+1}$

On differentiating w.r.t $x$, we get

$\frac{dy}{dx}=\frac{(x^2+1)\times 2x-x^2(2x+0)}{{(x^2+1)}^2}$

$\frac{dy}{dx}=\frac{2x^3+2x-2x^3}{{(x^2+1)}^2}$

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

Hence, the value is $\frac{2x}{{(x^2+1)}^2}$.