If you mean f(x) = ln(x²), then by the chain and power rules we have
[tex]f'(x) = \dfrac{(x^2)'}{x^2} = \dfrac{2x}{x^2} = \dfrac2x[/tex]
If you mean f(x) = ln(x)², then the same rules give
[tex]f'(x) = 2 \ln(x) \left(\ln(x)\right)' = 2\ln(x) \times \dfrac1x = \dfrac{2\ln(x)}x[/tex]
