Derivative of sech

Theorem: The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x}=-\mathrm{sech}(z)\mathrm{tanh}(z),$$ where $\mathrm{sech}$ denotes the hyperbolic secant and $\mathrm{tanh}$ denotes the hyperbolic tangent.

Proof: █