jika f(x) = x²-1, maka lim p→0 [tex] \frac{f(x + p) - f(x)}{p} [/tex] adalah...

f(x+p) = (x+p)^2 - 1 = x^2 + 2xp + p^2 - 1
maka
= ((x^2 + 2xp + p^2 - 1 - (x^2 - 1))/p
= (x^2 + 2xp + p^2 - 1 - x^2 + 1)/p
= (2xp + p^2)/p
= p(2x + p)/p
= 2x + p
= 2x