I need to differentiate the following function. Any help is greatly appreciated!
$\displaystyle
\sqrt {e^x - e^{-x}}
$
Are you familiar with the chain rule?
$\displaystyle \frac{dx}{dy}g[f(x)] = g'[f(x)]f'(x)$
Or let the variable be anything if that helps you think about it better...
$\displaystyle h = f($)
$\displaystyle h' = f'($)*'
Solution:
$\displaystyle g = \sqrt{u}$
$\displaystyle u = e^x - e^{-x}$
$\displaystyle u' = e^x+e^{-x}$
$\displaystyle g' = \frac{u'}{2\sqrt{u}} \Rightarrow \frac{e^x + e^{-x}}{2\sqrt{e^x - e^{-x}}}$