[tex] \lim_{x \to \ 2} \frac{f(x)-f(2)}{x-2}=f`(2)
[/tex]
[tex]f(x)=lnx- \frac{1}{x} [/tex]
[tex]f`(x)=(lnx)`- (\frac{1}{x})`= \frac{1}{x}- \frac{(1)`x-1*x`}{x^2}= \frac{1}{x}- \frac{-1}{x^2}= \frac{1}{x}+ \frac{1}{x^2}= \frac{x+1}{x^2} [/tex]
[tex]f`(2)= \frac{2+1}{2^2}= \frac{3}{4} [/tex]
