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.
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