Jika diketahui fungsi dibawah ini

a) f (x) = 3x + 2
f '(x) = limit {f (x + h) - f(x)}/ h
= limit { 3(x + h) +2 ) -(3x +2) }/ h
= limit { 3x +3h +2 - 3x -2 } / h
= limit 3h/ h
= limit 3 (h --> 0)
= 3
b) = limit { (x +h)^2 +3(x +h) -1 -(x^2 +3x -1} / h
= limit { x^2 +2xh +h^2 +3x +3h -1 -x^2-3x +1}/ h
= limit { 2xh +h^2 - 3h } / h
= limit ( 2x + h -3). (h -->0)
= 2x + 0 + 3
= 2x + 3