Question

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

Answer 1

`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)`