# Math Help - composite and quotient rules

1. ## 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)????

2. Let $f(u)=\ln u$ and $u=e^x+e^{-x}$

$\frac{df}{dx}=\frac{df}{du}\frac{du}{dx}=\frac{1}{ u}(e^x-e^{-x})=\frac{1}{e^x+e^{-x}}(e^x-e^{-x})$

3. does that mean that f ' (x) using the rules is therefore

1
______
(e^x - e ^-x)^2

4. No. The answer is given above.

5. The most compact form is $\tanh(x)$