Find the derivative of the function y = lnx/1+lnx?

Since the function is a quotient, we'll use the quotient
rule to differentiate the function with respect to
x:

`dy/dx = ((ln x)'*(1 + lnx) - (ln x)(1 + ln x)')/(1+ln
x)^2`

`dy/dx = (1/x + (lnx)/x - (ln x)/x)/(1+ln
x)^2`

We'll reduce like terms from
numerator:

`dy/dx = (1/x)/(1+ln
x)^2`

Therefore, the requested derivative of
the function is

`dy/dx = 1/(x*(1+ln
x)^2)`