Differentiate f(x) = 2xlnx.

Use the chain rule: f'(x) = v(du/dx) +u(dv/dx).

Let u = 2x, du/dx = 2, v = lnx, dv/dx = 1/x

Using this information: f'(x) = 2lnx + 2x/x

This simplifies to f'(x) = 2lnx +2.