# How do you differentiate (e^ (2x) - e^(-2x) ) ^ 2?

Dec 9, 2016

$4 \left({e}^{4 x} - {e}^{- 4 x}\right)$
First, differentiate "something" squared as $2 \times$ something. Then multiply by whatever you get by differentiating the something:
2(e^{2x}-e^{-2z})^1xx d/{dx}(e^{2x}-e^{-2x}) =2(e^{2x}-e^{-2z})xx(2e^{2x}+2e^{-2x}) (because $\frac{d}{\mathrm{dx}} \left({e}^{a x}\right) = a {e}^{a x}$)
$= 4 \left({e}^{2 x} - {e}^{- 2 x}\right) \left({e}^{2 x} + {e}^{- 2 x}\right)$.
Remember $\left(a - b\right) \left(a + b\right) = \left({a}^{2} - {b}^{2}\right)$ and ${e}^{2 x} \times {e}^{2 x} = {e}^{4 x}$