Question

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

Answer 1

Given : $f\left(x\right)=\frac{x+1}{x}$
$\Rightarrow f\left(x\right)=\frac{x}{x}+\frac{1}{x}$
$\Rightarrow f\left(x\right)=1+\frac{1}{x}$
$\Rightarrow f\left(x\right)=1+(x{)}^{-1}$
Differentitation with respect to $x$
$\Rightarrow f^{\prime }\left(x\right)=0+(-1)x^{-1-1}$
$\Rightarrow f^{\prime }\left(x\right)=0-x^{-2}$
$\Rightarrow f^{\prime }\left(x\right)=-x^{-2}$
$\Rightarrow f^{\prime }\left(x\right)=\frac{-1}{x^2}$