What is the derivative of the function y = tan^-1 (x lnx)

The derivative of arctan(x) = 1 / (1 + x^2). Using the chain rule, this needs to be multiplied by the derivative of (x ln(x)) as follows:

(1 / (1 + x^2)) [x(1/x) + ln(x))] = (1 + ln(x)) / (1 + x^2) <== answer

diff(arctan(x*ln(x)), x) = (ln(x) + 1)/(1 + x^2*ln(x)^2)