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Math Help - Derivate of exponential function

  1. #1
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    Derivate of exponential function

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

    <br />
\sqrt {e^x - e^{-x}}<br />
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  2. #2
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    Quote Originally Posted by hasanbalkan View Post
    I need to differentiate the following function. Any help is greatly appreciated!

    <br />
\sqrt {e^x - e^{-x}}<br />
    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}}}
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