Question

Evaluate d/dx (x/ Inx)=

Answer 1

Explanation:

f(x) = x/ln(x) = g(x)/h(x)

so, we need the quotient rule :

(g/h)' = (g'h - gh')/h²

f'(x) = (g'(x)×h(x) - g(x)×h'(x))/h²(x) =

= (1×ln(x) - x×(1/x))/ln²(x) =

= (ln(x) - 1)/ln²(x) = ln(x)/ln²(x) - 1/ln²(x) =

= 1/ln(x) - 1/ln²(x)