f(x) = 3·x^2 - 1
m = (f(x + h) - f(x)) / h
m = ((3·(x + h)^2 - 1) - (3·x^2 - 1)) / h
m = ((3·(x^2 + 2·h·x + h^2) - 1) - (3·x^2 - 1)) / h
m = ((3·x^2 + 6·h·x + 3·h^2 - 1) - (3·x^2 - 1)) / h
m = (6·h·x + 3·h^2) / h
m = 6·x + 3·h
Für den Grenzwert h --> 0 gilt jetzt
f'(x) = 6·x