Question

Differentiate $\frac{x^2+1}{x}$ w.r.t $x$

Answer 1

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

$\Rightarrow \frac{dy}{dx}=\frac{x\frac{d}{dx}(x^2+1)-(x^2+1)\frac{d}{dx}\left(x\right)}{x^2}$

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

$\Rightarrow \frac{dy}{dx}=\frac{2x^2-x^2-1}{x^2}$

$\Rightarrow \frac{dy}{dx}=\frac{x^2-1}{x^2}=1-\frac{1}{x^2}$