Question

for the function f(x)=lnx/5x find f"(x)

Answer 1

quotient rule

Answer 2

use quotient rule to get f'(x)

\[f'(x) = \frac{(1/x)5x - \ln x (5)}{(5x)^2} = \frac{1-\ln x}{5 x^2}\]
use quotient rule again to get f''(x)
\[f''(x) = \frac{(-1/x)(5x^2) - 10x(1-\ln x )}{(5x^2)^2} = \frac{2 \ln x -3}{5 x^3}\]