We need to find the derivative of \(\operatorname{sech}(x)\):
\[\frac{d}{dx}\operatorname{sech}(x) = \frac{d}{dx}\frac{1}{\cosh(x)}\]
If we derivative this:
\[\frac{d}{dx}\operatorname{sech}(x) = \frac{d}{dx} (\cosh(x))^{-1} = -(\cosh(x))^{-2} (\sinh(x)) \]
This means:
\[\frac{d}{dx}\operatorname{sech}(x) = -(\cosh(x))^{-1}(\tanh(x)) = -\operatorname{sech}(x)\tanh(x)\]