# What is the equation of the normal line of f(x)=1-x/lnx at x=2?

$y = - \frac{{\left(\ln 2\right)}^{2}}{1 - \ln 2} \cdot x + \frac{2 {\left(\ln 2\right)}^{2}}{1 - \ln 2} + 1 - \frac{2}{\ln} 2$

OR $y = - 1.565744172711 x + 1.2460982636442$

#### Explanation:

$f \left(x\right) = 1 - \frac{x}{\ln} x$
$f \left(2\right) = 1 - \frac{2}{\ln} 2$
$f ' \left(x\right) = - 1 \left(\frac{\ln x \cdot \left(1\right) - x \left(\frac{1}{x}\right) \left(1\right)}{\ln x} ^ 2\right)$

$f ' \left(2\right) = \frac{1 - \ln 2}{\ln 2} ^ 2$