Find the derivative of T(n)=n-n^3, using first principles.
Thanks.
$\displaystyle T^{\prime}(n) = \lim_{h \to 0} \frac{((n + h) - (n + h)^3) - (n - n^3)}{h}$
Expand the numerator and collect like terms. You will find that the resulting numerator is divisible by h, so divide the h in the numerator by the one in the denominator. This will make your limit trivial.
-Dan