[tex] \it f(x) = e^x-e^{-x}
\\ \\ \\
f'(x) = (e^x-e^{-x})' = (e^x)' - (e^{-x})' = e^x- (-x)'(e^{-x}) = e^x-(-1)e^{-x} =
\\ \\ \\
= e^x+e^{-x}=e^x+\dfrac{1}{e^x} [/tex]
[tex] \it \lim\limits_{x\to0} \dfrac{f(x)-f(0)}{x-0} = f'(0) = e^0+ \dfrac{1}{e^0}= 1+1=2 [/tex]
