d^2/dx^2 xlog(x)
Assuming "log" is the natural logarithm | Use instead

Derivative

d^2/dx^2(x log(x)) = 1/x

Plot

Plot
Plot

Roots

(no roots exist)

Indefinite integral

integral1/x dx = log(x) + constant
(assuming a complex-valued logarithm)

Limit

lim_(x-> ± ∞) 1/x = 0