Find the derivative of T(n)=n-n^3, using first principles.

Thanks.

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- Nov 24th 2007, 09:04 AMjohntuanDerrivative
Find the derivative of T(n)=n-n^3, using first principles.

Thanks. - Nov 24th 2007, 10:21 AMtopsquark
$\displaystyle T^{\prime}(n) = \lim_{h \to 0} \frac{((n + h) - (n + h)^3) - (n - n^3)}{h}$

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