Are you going to $\displaystyle F(x) = \frac{f(x)}{f'(x)}$ then $\displaystyle F(x) = \frac{\ln x}{\frac{1}{x}} = x\ln x$.
My professor wants us to graph F' without an equation. He wants us to use the graph of f(x) to graph F'. I'm confused and don't really know what to do for f(x) = lnx