2.3 Lösning 7

\[ f\,(a + h) = (a + h)^2 = a^2 + 2\,a\,h + h^2 \]

\( f(a) = a^2 \)

\[ {f(a+h) - f(a) \over h} = {a^2 + 2\,a\,h + h^2 - a^2 \over h} = {2\,a\,h + h^2 \over h} = {h\,(2\,a + h) \over h} = 2\,a + h \]

\[ f\,'(a) \; = \; \lim_{h \to 0} \; (2\,a + h) \; = \; 2\,a \]