Question

Find derivative of $f\left(x\right)=x+\frac{1}{x}+1$

• A. $\frac{(x+1)(x-1)}{x}$
• B. $\frac{(x+1)(x-1)}{x^2}$
• C. $\frac{(1+x)(1-x)}{x^2}$
• D. $\text{None of these}$

Answer 1

The correct option is B $\frac{(x+1)(x-1)}{x^2}$

Given $f\left(x\right)=x+\frac{1}{x}+1$
$\therefore \text{Derivative will be}\frac{df\left(x\right)}{dx}=\frac{d}{dx}(x+\frac{1}{x}+1)$
$=\frac{dx}{dx}+\frac{d{x}^{-1}}{dx}+\frac{d1}{dx}$
$=1+(-1x^{-}2)+0$
$=1-\frac{1}{x^2}+0$
$=\frac{x^2-1}{x^2}$
$=\frac{(x+1)(x-1)}{x^2}$