1. Derivate of exponential function

I need to differentiate the following function. Any help is greatly appreciated!

$
\sqrt {e^x - e^{-x}}
$

2. Originally Posted by hasanbalkan
I need to differentiate the following function. Any help is greatly appreciated!

$
\sqrt {e^x - e^{-x}}
$
Are you familiar with the chain rule?

$\frac{dx}{dy}g[f(x)] = g'[f(x)]f'(x)$

Or let the variable be anything if that helps you think about it better...
$h = f($)
$h' = f'($)*'

Solution:

$g = \sqrt{u}$
$u = e^x - e^{-x}$
$u' = e^x+e^{-x}$

$g' = \frac{u'}{2\sqrt{u}} \Rightarrow \frac{e^x + e^{-x}}{2\sqrt{e^x - e^{-x}}}$