# How do you differentiate s=(t^2-1)(t^2+1)?

Nov 14, 2016

$4 {t}^{3}$

#### Explanation:

First you open the bracket and multiply the two terms,

$s = \left({t}^{2} - 1\right) \left({t}^{2} + 1\right)$
$s = {t}^{4} + {t}^{2} - {t}^{2} - 1$
$s = {t}^{4} - 1$

Now, differentiate for t.

$\frac{\mathrm{ds}}{\mathrm{dt}}$ = $4 \cdot {t}^{4 - 1} - 0$ = $4 {t}^{3}$