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f = log(x)^2-log(x)
show(f(x=3).substitute_function({log(x):function('ln')(x)}))
show(f.diff().substitute_function({log(x):function('ln')(x)}))

Shows $\ln(3)^2-\ln(3)$ and $\frac{2\ln(x)}{x}-\frac{1}{x}$.