# How do you find the derivative of (e^(2*x)-e^(-2*x))/(e^(2*x)+e^(-2*x))?

Apr 3, 2018

$2 \left(1 - {\left({e}^{\left(2. x\right) - {e}^{- 2. x}} / \left({e}^{2. x} + {e}^{- 2. x}\right)\right)}^{2}\right)$

#### Explanation:

isn't that just $\tanh 2 x$?

and the derivative of $\tanh x$ = $1 - {\left(\tanh x\right)}^{2}$
http://math2.org/math/derivatives/more/hyperbolics.htm

thus the derivative of
$\tanh 2 x$

is

$2 \left(1 - {\left(\tanh x\right)}^{2}\right)$