# What is the derivative of sqrt(e^(2x) +e^(-2x))?

$\frac{1}{2} {\left({e}^{2 x} + {e}^{- 2 x}\right)}^{- \frac{1}{2}} \cdot \left(2 {e}^{2 x} - 2 {e}^{- 2 x}\right)$
$\frac{d}{\mathrm{dx}} \sqrt{{e}^{2 x} + {e}^{- 2 x}} = \frac{d}{\mathrm{dx}} {\left({e}^{2 x} + {e}^{- 2 x}\right)}^{\frac{1}{2}}$
$= \frac{1}{2} {\left({e}^{2 x} + {e}^{- 2 x}\right)}^{- \frac{1}{2}} \cdot \left(2 {e}^{2 x} - 2 {e}^{- 2 x}\right)$