How do you differentiate $(e^x - e^(-x))/(e^x + e^(-x))$ ?

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Answer 1 · 2015-04-16T13:18:55

$sech^2x$

The given expression is equivalent to tanh x. Its derivative is $sech^2x$ or $1/cosh^2x$ .

Since cosh x = $(e^x +e^-x)/2$ , the derivative can also be expressed as $4/(e^(2x) +e^(-2x) +2)$

How do you differentiate (e^x - e^(-x))/(e^x + e^(-x))(e^x - e^(-x))/(e^x + e^(-x))?