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Math Help - composite and quotient rules

  1. #1
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    composite and quotient rules

    the function of f is

    f(x)= ln(e^x + e^-x)

    using composite and quotient rules give an expression for
    f ' (x) and f ''(x)

    im confused about these rules....isnt f ' (x) just 1/e^x + e ^-x)????
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  2. #2
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    Let f(u)=\ln u and u=e^x+e^{-x}

    \frac{df}{dx}=\frac{df}{du}\frac{du}{dx}=\frac{1}{  u}(e^x-e^{-x})=\frac{1}{e^x+e^{-x}}(e^x-e^{-x})
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  3. #3
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    does that mean that f ' (x) using the rules is therefore

    1
    ______
    (e^x - e ^-x)^2
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  4. #4
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    No. The answer is given above.
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  5. #5
    Member Ruun's Avatar
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    The most compact form is \tanh(x)
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