Single Variable Calculus, Chapter 7, 7.2-1, Section 7.2-1, Problem 42

Differentiate the function $\displaystyle y = \frac{e^u - e^{-u}}{e^u + e^{-u}}$


$
\begin{equation}
\begin{aligned}

\text{if } y = \frac{e^u - e^{-4}}{e^u + e^{-u}} \text{ then by using Quotient Rule}
\\
\\
y' =& \frac{(e^u + e^{-u}) (e^u - e^{-u} (1)) - (e^u - e^{-u})(e^u + e^{-u} (-1)) }{(e^u + e^{-u})^2}
\\
\\
y' =& \frac{(e^u + e^{-u})^2 - (e^u - e^{-u})^2}{(e^u + e^{-u})^2}
\\
\\
y' =& \frac{e^{2u} + 2 + e^{-2u} - e^{2u} + 2 - e^{-2u} }{(e^u + e^{-u})^2}
\\
\\
y' =& \frac{4}{(e^u + e^{-u})^2}

\end{aligned}
\end{equation}
$