Question

How do you use the quotient rule to find the derivative of `y=x/ln(x)` ?

Answer 1

`y'=(lnx-1)/(lnx)^2`

Explanation

Suppose,

`y=f(x)/g(x)`

Using Quotient Rule, which is

`y'=(f'(x)g(x)-f(x)g'(x))/(g(x))^2`

Similarly, following for the given problem `y=x/lnx` and differentiating with respect to `x`, yields

`y'=((x)'(lnx)-x(lnx)')/(lnx)^2`

`y'=(lnx-x*1/x)/(lnx)^2`

`y'=(lnx-1)/(lnx)^2`