f este derivabila in x0 daca exista f'(x0) = [tex] \lim_{x \to \ x0} \frac{f(x)-f(x0)}{x-x0} [/tex] si e finita
f'(1) = [tex] \lim_{x \to \ 1} \frac{ln(x^{2}+2x) -ln3}{x-1} = \lim_{x \to \ 1} \frac{ln( \frac{ x^{2}+2x }{3} )}{x-1}=^{l'H} \lim_{x \to \ 1} \frac{2x+2}{ x^{2}+2x }= \frac{4}{3} [/tex]
deci f este derivabila in x0 = 1 si f'(1) = [tex] \frac{4}{3} [/tex]
