Question

Differentiate the following functions with respect to ${}^{\prime }{x}^{\prime }$
$\frac{x^2+1}{x+1}$

Answer 1

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

On differentiating wrt x we get

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

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